LMFDB - Embedded newform 207.4.m.a.4.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,4,Mod(4,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([22, 12])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.4"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.m (of order $33$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$1400$
Relative dimension:	$70$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			4.17
Character	$\chi$	$=$	207.4
Dual form			207.4.m.a.52.17

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.98001 + 2.78054i) q^{2} +(-4.08591 - 3.21019i) q^{3} +(-1.19440 - 3.45100i) q^{4} +(13.0530 - 6.72929i) q^{5} +(17.0162 - 5.00482i) q^{6} +(11.9856 - 9.42560i) q^{7} +(-14.2411 - 4.18156i) q^{8} +(6.38935 + 26.2331i) q^{9} +(-7.13406 + 49.6185i) q^{10} +(6.23048 - 0.594938i) q^{11} +(-6.19815 + 17.9348i) q^{12} +(-40.3193 - 31.7074i) q^{13} +(2.47656 + 51.9893i) q^{14} +(-74.9357 - 14.4073i) q^{15} +(62.7890 - 49.3778i) q^{16} +(-11.3488 - 13.0972i) q^{17} +(-85.5932 - 34.1761i) q^{18} +(-90.1240 + 104.009i) q^{19} +(-38.8134 - 37.0085i) q^{20} +(-79.2302 + 0.0360241i) q^{21} +(-10.6822 + 18.5021i) q^{22} +(-52.7895 - 96.8518i) q^{23} +(44.7643 + 62.8022i) q^{24} +(52.5904 - 73.8528i) q^{25} +(167.996 - 49.3282i) q^{26} +(58.1070 - 127.697i) q^{27} +(-46.8435 - 30.1045i) q^{28} +(53.0252 - 153.206i) q^{29} +(188.434 - 179.835i) q^{30} +(198.779 - 189.535i) q^{31} +(7.32410 + 153.752i) q^{32} +(-27.3670 - 17.5702i) q^{33} +(58.8881 - 5.62313i) q^{34} +(93.0208 - 203.687i) q^{35} +(82.8991 - 53.3826i) q^{36} +(-312.529 + 200.850i) q^{37} +(-110.753 - 456.532i) q^{38} +(62.9541 + 258.986i) q^{39} +(-214.028 + 41.2505i) q^{40} +(345.745 - 178.244i) q^{41} +(156.777 - 220.374i) q^{42} +(-86.6292 - 82.6007i) q^{43} +(-9.49484 - 20.7908i) q^{44} +(259.930 + 299.425i) q^{45} +(373.824 + 44.9844i) q^{46} +(-178.430 - 309.050i) q^{47} +(-415.062 + 0.188719i) q^{48} +(-26.0520 + 107.388i) q^{49} +(101.221 + 292.459i) q^{50} +(4.32564 + 89.9459i) q^{51} +(-61.2649 + 177.013i) q^{52} +(-44.5682 - 309.979i) q^{53} +(240.015 + 414.411i) q^{54} +(77.3229 - 49.6924i) q^{55} +(-210.102 + 84.1122i) q^{56} +(702.126 - 135.655i) q^{57} +(321.005 + 450.789i) q^{58} +(-652.520 - 513.147i) q^{59} +(39.7837 + 275.812i) q^{60} +(-0.310472 - 1.27978i) q^{61} +(133.426 + 927.996i) q^{62} +(323.843 + 254.197i) q^{63} +(95.5716 + 61.4201i) q^{64} +(-739.656 - 142.557i) q^{65} +(103.042 - 41.3060i) q^{66} +(121.776 + 11.6282i) q^{67} +(-31.6435 + 54.8081i) q^{68} +(-95.2192 + 565.192i) q^{69} +(382.178 + 661.951i) q^{70} +(-286.115 - 626.503i) q^{71} +(18.7041 - 400.306i) q^{72} +(349.522 - 403.370i) q^{73} +(60.3397 - 1266.69i) q^{74} +(-451.961 + 132.931i) q^{75} +(466.579 + 186.790i) q^{76} +(69.0685 - 65.8567i) q^{77} +(-844.772 - 337.750i) q^{78} +(-757.094 + 303.095i) q^{79} +(487.307 - 1067.05i) q^{80} +(-647.352 + 335.225i) q^{81} +(-188.965 + 1314.28i) q^{82} +(82.8133 + 42.6932i) q^{83} +(94.7572 + 273.381i) q^{84} +(-236.271 - 94.5886i) q^{85} +(401.202 - 77.3253i) q^{86} +(-708.477 + 455.766i) q^{87} +(-91.2166 - 17.5806i) q^{88} +(516.250 - 151.585i) q^{89} +(-1347.23 + 129.881i) q^{90} -782.113 q^{91} +(-271.184 + 297.857i) q^{92} +(-1420.64 + 136.306i) q^{93} +(1212.62 + 115.791i) q^{94} +(-476.484 + 1964.09i) q^{95} +(463.647 - 651.728i) q^{96} +(3.64256 - 76.4668i) q^{97} +(-247.013 - 285.068i) q^{98} +(55.4158 + 159.644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) $ 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.98001	+	2.78054i	−0.700040	+	0.983069i	0.299539	+	0.954084i	$0.403167\pi$
$2$	−1.98001	+	2.78054i	−0.700040	+	0.983069i	−0.999580	+	0.0289853i	$0.990772\pi$
$3$	−4.08591	−	3.21019i	−0.786334	−	0.617802i
$3$	−4.08591	−	3.21019i	−0.786334	−	0.617802i
$4$	−1.19440	−	3.45100i	−0.149301	−	0.431375i
$5$	13.0530	−	6.72929i	1.16750	−	0.601886i	0.238198	−	0.971217i	$-0.423443\pi$
$5$	13.0530	−	6.72929i	1.16750	−	0.601886i	0.929298	+	0.369331i	$0.120413\pi$
$6$	17.0162	−	5.00482i	1.15781	−	0.340535i
$7$	11.9856	−	9.42560i	0.647163	−	0.508935i	−0.239772	−	0.970829i	$-0.577073\pi$
$7$	11.9856	−	9.42560i	0.647163	−	0.508935i	0.886935	+	0.461895i	$0.152830\pi$
$8$	−14.2411	−	4.18156i	−0.629374	−	0.184801i
$9$	6.38935	+	26.2331i	0.236643	+	0.971597i
$10$	−7.13406	+	49.6185i	−0.225599	+	1.56907i
$11$	6.23048	−	0.594938i	0.170778	−	0.0163073i	−0.00931663	−	0.999957i	$-0.502966\pi$
$11$	6.23048	−	0.594938i	0.170778	−	0.0163073i	0.180095	+	0.983649i	$0.442360\pi$
$12$	−6.19815	+	17.9348i	−0.149104	+	0.431443i
$13$	−40.3193	−	31.7074i	−0.860196	−	0.676466i	0.0873175	−	0.996181i	$-0.472171\pi$
$13$	−40.3193	−	31.7074i	−0.860196	−	0.676466i	−0.947514	+	0.319715i	$0.896413\pi$
$14$	2.47656	+	51.9893i	0.0472777	+	0.992481i
$15$	−74.9357	−	14.4073i	−1.28989	−	0.247997i
$16$	62.7890	−	49.3778i	0.981078	−	0.771528i
$17$	−11.3488	−	13.0972i	−0.161911	−	0.186855i	0.668997	−	0.743265i	$-0.266724\pi$
$17$	−11.3488	−	13.0972i	−0.161911	−	0.186855i	−0.830908	+	0.556410i	$0.812178\pi$
$18$	−85.5932	−	34.1761i	−1.12081	−	0.447521i
$19$	−90.1240	+	104.009i	−1.08820	+	1.25585i	−0.123547	+	0.992339i	$0.539427\pi$
$19$	−90.1240	+	104.009i	−1.08820	+	1.25585i	−0.964655	+	0.263514i	$0.915118\pi$
$20$	−38.8134	−	37.0085i	−0.433947	−	0.413767i
$21$	−79.2302	+	0.0360241i	−0.823307	+	0.000374338i
$22$	−10.6822	+	18.5021i	−0.103520	+	0.179303i
$23$	−52.7895	−	96.8518i	−0.478582	−	0.878043i
$23$	−52.7895	−	96.8518i	−0.478582	−	0.878043i
$24$	44.7643	+	62.8022i	0.380728	+	0.534143i
$25$	52.5904	−	73.8528i	0.420723	−	0.590823i
$26$	167.996	−	49.3282i	1.26719	−	0.372079i
$27$	58.1070	−	127.697i	0.414174	−	0.910198i
$28$	−46.8435	−	30.1045i	−0.316164	−	0.203186i
$29$	53.0252	−	153.206i	0.339535	−	0.981023i	−0.637960	−	0.770069i	$-0.720222\pi$
$29$	53.0252	−	153.206i	0.339535	−	0.981023i	0.977496	−	0.210954i	$-0.0676571\pi$
$30$	188.434	−	179.835i	1.14677	−	1.09444i
$31$	198.779	−	189.535i	1.15167	−	1.09812i	0.157810	−	0.987469i	$-0.449557\pi$
$31$	198.779	−	189.535i	1.15167	−	1.09812i	0.993860	−	0.110646i	$-0.0352919\pi$
$32$	7.32410	+	153.752i	0.0404603	+	0.849367i
$33$	−27.3670	−	17.5702i	−0.144363	−	0.0926840i
$34$	58.8881	−	5.62313i	0.297036	−	0.0283635i
$35$	93.0208	−	203.687i	0.449239	−	0.983697i
$36$	82.8991	−	53.3826i	0.383792	−	0.247142i
$37$	−312.529	+	200.850i	−1.38864	+	0.892422i	−0.999585	−	0.0287945i	$-0.990833\pi$
$37$	−312.529	+	200.850i	−1.38864	+	0.892422i	−0.389050	+	0.921216i	$0.627197\pi$
$38$	−110.753	−	456.532i	−0.472804	−	1.94893i
$39$	62.9541	+	258.986i	0.258480	+	1.06336i
$40$	−214.028	+	41.2505i	−0.846020	+	0.163057i
$41$	345.745	−	178.244i	1.31698	−	0.678951i	0.350712	−	0.936484i	$-0.385940\pi$
$41$	345.745	−	178.244i	1.31698	−	0.678951i	0.966270	+	0.257533i	$0.0829095\pi$
$42$	156.777	−	220.374i	0.575980	−	0.809630i
$43$	−86.6292	−	82.6007i	−0.307228	−	0.292942i	0.520741	−	0.853715i	$-0.325656\pi$
$43$	−86.6292	−	82.6007i	−0.307228	−	0.292942i	−0.827970	+	0.560773i	$0.810504\pi$
$44$	−9.49484	−	20.7908i	−0.0325318	−	0.0712348i
$45$	259.930	+	299.425i	0.861070	+	0.991903i
$46$	373.824	+	44.9844i	1.19820	+	0.144187i
$47$	−178.430	−	309.050i	−0.553760	−	0.959141i	−0.997999	−	0.0632326i	$-0.979859\pi$
$47$	−178.430	−	309.050i	−0.553760	−	0.959141i	0.444238	−	0.895909i	$-0.353474\pi$
$48$	−415.062	+	0.188719i	−1.24811	+	0.000567485i
$49$	−26.0520	+	107.388i	−0.0759535	+	0.313084i
$50$	101.221	+	292.459i	0.286297	+	0.827200i
$51$	4.32564	+	89.9459i	0.0118767	+	0.246960i
$52$	−61.2649	+	177.013i	−0.163383	+	0.472064i
$53$	−44.5682	−	309.979i	−0.115508	−	0.803375i	−0.962405	−	0.271618i	$-0.912441\pi$
$53$	−44.5682	−	309.979i	−0.115508	−	0.803375i	0.846897	−	0.531757i	$-0.178468\pi$
$54$	240.015	+	414.411i	0.604849	+	1.04434i
$55$	77.3229	−	49.6924i	0.189568	−	0.121828i
$56$	−210.102	+	84.1122i	−0.501359	+	0.200714i
$57$	702.126	−	135.655i	1.63156	−	0.315227i
$58$	321.005	+	450.789i	0.726725	+	1.02054i
$59$	−652.520	−	513.147i	−1.43984	−	1.13231i	−0.968098	−	0.250573i	$-0.919381\pi$
$59$	−652.520	−	513.147i	−1.43984	−	1.13231i	−0.471747	−	0.881734i	$-0.656376\pi$
$60$	39.7837	+	275.812i	0.0856010	+	0.593452i
$61$	−0.310472	−	1.27978i	−0.000651669	−	0.00268622i	0.971485	−	0.237102i	$-0.0761975\pi$
$61$	−0.310472	−	1.27978i	−0.000651669	−	0.00268622i	−0.972136	+	0.234416i	$0.924682\pi$
$62$	133.426	+	927.996i	0.273308	+	1.90090i
$63$	323.843	+	254.197i	0.647625	+	0.508346i
$64$	95.5716	+	61.4201i	0.186663	+	0.119961i
$65$	−739.656	−	142.557i	−1.41143	−	0.272031i
$66$	103.042	−	41.3060i	0.192175	−	0.0770366i
$67$	121.776	+	11.6282i	0.222049	+	0.0212031i	0.205488	−	0.978660i	$-0.434122\pi$
$67$	121.776	+	11.6282i	0.222049	+	0.0212031i	0.0165616	+	0.999863i	$0.494728\pi$
$68$	−31.6435	+	54.8081i	−0.0564314	+	0.0977421i
$69$	−95.2192	+	565.192i	−0.166131	+	0.986104i
$70$	382.178	+	661.951i	0.652557	+	1.13026i
$71$	−286.115	−	626.503i	−0.478247	−	1.04722i	−0.982942	−	0.183917i	$-0.941122\pi$
$71$	−286.115	−	626.503i	−0.478247	−	1.04722i	0.504695	−	0.863298i	$-0.331605\pi$
$72$	18.7041	−	400.306i	0.0306152	−	0.655229i
$73$	349.522	−	403.370i	0.560390	−	0.646725i	−0.402882	−	0.915252i	$-0.631991\pi$
$73$	349.522	−	403.370i	0.560390	−	0.646725i	0.963272	+	0.268527i	$0.0865369\pi$
$74$	60.3397	−	1266.69i	0.0947885	−	1.98986i
$75$	−451.961	+	132.931i	−0.695840	+	0.204661i
$76$	466.579	+	186.790i	0.704213	+	0.281925i
$77$	69.0685	−	65.8567i	0.102222	−	0.0974684i
$78$	−844.772	−	337.750i	−1.22630	−	0.490290i
$79$	−757.094	+	303.095i	−1.07822	+	0.431656i	−0.841687	−	0.539966i	$-0.818437\pi$
$79$	−757.094	+	303.095i	−1.07822	+	0.431656i	−0.236538	+	0.971622i	$0.576013\pi$
$80$	487.307	−	1067.05i	0.681032	−	1.49125i
$81$	−647.352	+	335.225i	−0.888001	+	0.459842i
$82$	−188.965	+	1314.28i	−0.254484	+	1.76998i
$83$	82.8133	+	42.6932i	0.109517	+	0.0564601i	0.512115	−	0.858917i	$-0.328862\pi$
$83$	82.8133	+	42.6932i	0.109517	+	0.0564601i	−0.402597	+	0.915377i	$0.631893\pi$
$84$	94.7572	+	273.381i	0.123082	+	0.355098i
$85$	−236.271	−	94.5886i	−0.301496	−	0.120701i
$86$	401.202	−	77.3253i	0.503054	−	0.0969558i
$87$	−708.477	+	455.766i	−0.873066	+	0.561647i
$88$	−91.2166	−	17.5806i	−0.110497	−	0.0212965i
$89$	516.250	−	151.585i	0.614859	−	0.180539i	0.0405498	−	0.999178i	$-0.487089\pi$
$89$	516.250	−	151.585i	0.614859	−	0.180539i	0.574309	+	0.818639i	$0.305271\pi$
$90$	−1347.23	+	129.881i	−1.57789	+	0.152119i
$91$	−782.113			−0.900964
$92$	−271.184	+	297.857i	−0.307314	+	0.337541i
$93$	−1420.64	+	136.306i	−1.58401	+	0.151982i
$94$	1212.62	+	115.791i	1.33056	+	0.127053i
$95$	−476.484	+	1964.09i	−0.514592	+	2.12118i
$96$	463.647	−	651.728i	0.492925	−	0.692883i
$97$	3.64256	−	76.4668i	0.00381285	−	0.0800415i	−0.996159	−	0.0875645i	$-0.972092\pi$
$97$	3.64256	−	76.4668i	0.00381285	−	0.0800415i	0.999972	+	0.00752293i	$0.00239465\pi$
$98$	−247.013	−	285.068i	−0.254613	−	0.293839i
$99$	55.4158	+	159.644i	0.0562575	+	0.162068i
$100$	−317.681	−	93.2794i	−0.317681	−	0.0932794i
$101$	811.298	+	418.253i	0.799279	+	0.412057i	0.808936	−	0.587897i	$-0.200044\pi$
$101$	811.298	+	418.253i	0.799279	+	0.412057i	−0.00965743	+	0.999953i	$0.503074\pi$
$102$	−258.663	−	166.066i	−0.251093	−	0.161206i
$103$	−541.160	−	759.953i	−0.517690	−	0.726994i	0.470129	−	0.882598i	$-0.344207\pi$
$103$	−541.160	−	759.953i	−0.517690	−	0.726994i	−0.987820	+	0.155603i	$0.950268\pi$
$104$	441.604	+	620.146i	0.416374	+	0.584715i
$105$	−1033.95	+	533.633i	−0.960982	+	0.495974i
$106$	950.154	+	489.839i	0.870634	+	0.448843i
$107$	−380.582	−	111.749i	−0.343853	−	0.100964i	0.105246	−	0.994446i	$-0.466437\pi$
$107$	−380.582	−	111.749i	−0.343853	−	0.100964i	−0.449099	+	0.893482i	$0.648255\pi$
$108$	−510.087	−	48.0054i	−0.454473	−	0.0427715i
$109$	1110.68	+	1281.79i	0.975998	+	1.12636i	0.991968	+	0.126490i	$0.0403711\pi$
$109$	1110.68	+	1281.79i	0.975998	+	1.12636i	−0.0159695	+	0.999872i	$0.505083\pi$
$110$	−14.9287	+	313.391i	−0.0129399	+	0.271642i
$111$	1921.74	+	182.622i	1.64327	+	0.156159i
$112$	287.150	−	1183.65i	0.242260	−	0.998609i
$113$	627.861	+	59.9535i	0.522692	+	0.0499111i	0.353068	−	0.935598i	$-0.385138\pi$
$113$	627.861	+	59.9535i	0.522692	+	0.0499111i	0.169624	+	0.985509i	$0.445745\pi$
$114$	−1013.03	+	2220.89i	−0.832268	+	1.82461i
$115$	−1340.81	−	908.970i	−1.08722	−	0.737060i
$116$	−592.049			−0.473882
$117$	574.171	−	1260.29i	0.453693	−	0.995845i
$118$	2718.82	−	798.319i	2.12109	−	0.622807i
$119$	−259.472	−	50.0091i	−0.199880	−	0.0385237i
$120$	1006.92	+	518.525i	0.765991	+	0.394455i
$121$	−1268.48	+	244.480i	−0.953029	+	0.183681i
$122$	4.17322	+	1.67071i	0.00309693	+	0.00123983i
$123$	−1984.88	−	381.618i	−1.45504	−	0.279751i
$124$	−891.510	−	459.605i	−0.645645	−	0.332853i
$125$	−71.7607	+	499.107i	−0.0513478	+	0.357132i
$126$	−1348.02	+	397.146i	−0.953103	+	0.280798i
$127$	429.221	−	939.863i	0.299899	−	0.656688i	−0.698355	−	0.715752i	$-0.746084\pi$
$127$	429.221	−	939.863i	0.299899	−	0.656688i	0.998254	+	0.0590638i	$0.0188115\pi$
$128$	−1503.22	+	601.797i	−1.03802	+	0.415561i
$129$	88.7950	+	615.596i	0.0606044	+	0.420156i
$130$	1860.91	−	1774.38i	1.25548	−	1.19710i
$131$	965.549	+	386.548i	0.643973	+	0.257808i	0.670579	−	0.741838i	$-0.266046\pi$
$131$	965.549	+	386.548i	0.643973	+	0.257808i	−0.0266061	+	0.999646i	$0.508470\pi$
$132$	−27.9474	+	115.430i	−0.0184281	+	0.0761126i
$133$	−99.8486	+	2096.08i	−0.0650975	+	1.36657i
$134$	−273.450	+	315.579i	−0.176287	+	0.203447i
$135$	−100.841	−	2057.85i	−0.0642890	−	1.31194i
$136$	106.853	+	233.975i	0.0673716	+	0.147523i
$137$	274.692	+	475.781i	0.171303	+	0.296706i	0.938876	−	0.344256i	$-0.111869\pi$
$137$	274.692	+	475.781i	0.171303	+	0.296706i	−0.767573	+	0.640962i	$0.778536\pi$
$138$	−1383.00	−	1383.85i	−0.853110	−	0.853631i
$139$	1361.73	−	2358.59i	0.830939	−	1.43923i	−0.0663549	−	0.997796i	$-0.521137\pi$
$139$	1361.73	−	2358.59i	0.830939	−	1.43923i	0.897294	−	0.441433i	$-0.145530\pi$
$140$	−814.029	−	77.7304i	−0.491415	−	0.0469244i
$141$	−263.060	+	1835.55i	−0.157118	+	1.09632i
$142$	2308.53	+	444.932i	1.36428	+	0.262943i
$143$	−270.072	−	173.565i	−0.157934	−	0.101498i
$144$	1696.51	+	1331.66i	0.981779	+	0.770636i
$145$	−338.831	−	2356.62i	−0.194058	−	1.34970i
$146$	429.528	+	1770.54i	0.243479	+	1.00364i
$147$	451.182	−	355.146i	0.253149	−	0.199265i
$148$	1066.42	+	838.644i	0.592293	+	0.465784i
$149$	1628.29	+	2286.61i	0.895266	+	1.25722i	0.965687	+	0.259707i	$0.0836261\pi$
$149$	1628.29	+	2286.61i	0.895266	+	1.25722i	−0.0704217	+	0.997517i	$0.522434\pi$
$150$	525.269	−	1519.90i	0.285920	−	0.827330i
$151$	−587.190	+	235.075i	−0.316456	+	0.126690i	−0.524452	−	0.851440i	$-0.675730\pi$
$151$	−587.190	+	235.075i	−0.316456	+	0.126690i	0.207997	+	0.978130i	$0.433306\pi$
$152$	1718.38	−	1104.34i	0.916969	−	0.589300i
$153$	271.069	−	381.397i	0.143233	−	0.201530i
$154$	46.3606	+	322.445i	0.0242587	+	0.168723i
$155$	1319.22	−	3811.65i	0.683630	−	1.97522i
$156$	818.570	−	526.589i	0.420116	−	0.270262i
$157$	486.369	+	1405.27i	0.247238	+	0.714349i	0.998521	+	0.0543679i	$0.0173144\pi$
$157$	486.369	+	1405.27i	0.247238	+	0.714349i	−0.751282	+	0.659981i	$0.770564\pi$
$158$	656.290	−	2705.26i	0.330453	−	1.36215i
$159$	−812.990	+	1409.62i	−0.405499	+	0.703082i
$160$	1130.24	+	1957.64i	0.558459	+	0.967280i
$161$	−1545.60	−	663.256i	−0.756587	−	0.324670i
$162$	349.660	−	2463.74i	0.169580	−	1.19487i
$163$	853.530	+	1868.97i	0.410145	+	0.898092i	0.996140	+	0.0877775i	$0.0279765\pi$
$163$	853.530	+	1868.97i	0.410145	+	0.898092i	−0.585995	+	0.810315i	$0.699296\pi$
$164$	−1028.08	−	980.271i	−0.489509	−	0.466746i
$165$	−475.457	−	45.1825i	−0.224329	−	0.0213179i
$166$	−282.682	+	145.732i	−0.132171	+	0.0681388i
$167$	−198.565	+	38.2703i	−0.0920085	+	0.0177332i	−0.235048	−	0.971984i	$-0.575525\pi$
$167$	−198.565	+	38.2703i	−0.0920085	+	0.0177332i	0.143039	+	0.989717i	$0.454313\pi$
$168$	1128.48	+	330.793i	0.518237	+	0.151912i
$169$	102.320	+	421.770i	0.0465728	+	0.191976i
$170$	730.827	−	469.674i	0.329717	−	0.211896i
$171$	−3304.30	−	1699.68i	−1.47770	−	0.760106i
$172$	−181.585	+	397.616i	−0.0804985	+	0.176267i
$173$	3415.57	−	326.147i	1.50105	−	0.143333i	0.688076	−	0.725638i	$-0.258455\pi$
$173$	3415.57	−	326.147i	1.50105	−	0.143333i	0.812970	+	0.582306i	$0.197849\pi$
$174$	135.519	−	2872.37i	0.0590441	−	1.25146i
$175$	−65.7789	−	1380.87i	−0.0284138	−	0.596479i
$176$	361.829	−	345.003i	0.154965	−	0.147759i
$177$	1018.84	+	4191.39i	0.432658	+	1.77991i
$178$	−600.695	+	1735.59i	−0.252944	+	0.730833i
$179$	−1747.61	−	1123.12i	−0.729736	−	0.468973i	0.122275	−	0.992496i	$-0.460981\pi$
$179$	−1747.61	−	1123.12i	−0.729736	−	0.468973i	−0.852011	+	0.523523i	$0.824617\pi$
$180$	722.855	−	1254.66i	0.299325	−	0.519536i
$181$	−3614.11	+	1061.20i	−1.48417	+	0.435792i	−0.920676	−	0.390328i	$-0.872361\pi$
$181$	−3614.11	+	1061.20i	−1.48417	+	0.435792i	−0.563494	+	0.826120i	$0.690543\pi$
$182$	1548.59	−	2174.70i	0.630711	−	0.885710i
$183$	−2.83978	+	6.22575i	−0.00114712	+	0.00251487i
$184$	346.789	+	1600.02i	0.138944	+	0.641059i
$185$	−2727.87	+	4724.80i	−1.08409	+	1.87770i
$186$	2433.88	−	4220.03i	0.959466	−	1.66359i
$187$	−78.5005	−	74.8501i	−0.0306980	−	0.0292705i
$188$	−853.416	+	984.895i	−0.331073	+	0.382079i
$189$	−507.174	−	2078.22i	−0.195193	−	0.799834i
$190$	−4517.80	−	5213.82i	−1.72503	−	1.99079i
$191$	−763.465	+	600.396i	−0.289227	+	0.227451i	−0.752221	−	0.658911i	$-0.771018\pi$
$191$	−763.465	+	600.396i	−0.289227	+	0.227451i	0.462994	+	0.886361i	$0.346775\pi$
$192$	−193.327	−	557.760i	−0.0726675	−	0.209650i
$193$	−196.987	−	4135.26i	−0.0734685	−	1.54229i	−0.671611	−	0.740904i	$-0.734397\pi$
$193$	−196.987	−	4135.26i	−0.0734685	−	1.54229i	0.598142	−	0.801390i	$-0.295906\pi$
$194$	205.407	+	161.534i	0.0760172	+	0.0597806i
$195$	2564.53	+	2956.91i	0.941795	+	1.08589i
$196$	401.713	−	38.3589i	0.146397	−	0.0139792i
$197$	88.1090	−	612.812i	0.0318655	−	0.221630i	−0.967666	−	0.252235i	$-0.918834\pi$
$197$	88.1090	−	612.812i	0.0318655	−	0.221630i	0.999532	+	0.0306053i	$0.00974351\pi$
$198$	−553.619	−	162.011i	−0.198707	−	0.0581494i
$199$	2968.06	+	871.500i	1.05729	+	0.310447i	0.763758	−	0.645503i	$-0.223352\pi$
$199$	2968.06	+	871.500i	1.05729	+	0.310447i	0.293528	+	0.955950i	$0.405170\pi$
$200$	−1057.77	+	831.836i	−0.373976	+	0.294098i
$201$	−460.237	−	438.436i	−0.161505	−	0.153855i
$202$	−2769.35	+	1427.70i	−0.964608	+	0.497290i
$203$	−808.520	−	2336.07i	−0.279542	−	0.807683i
$204$	305.237	−	122.360i	0.104759	−	0.0419945i
$205$	3313.55	−	4653.23i	1.12892	−	1.58534i
$206$	3184.58			1.07709
$207$	2203.43	−	2003.65i	0.739851	−	0.672771i
$208$	−4097.25			−1.36583
$209$	−499.637	+	701.641i	−0.165362	+	0.232218i
$210$	563.445	−	3931.54i	0.185150	−	1.29191i
$211$	1617.52	+	4673.51i	0.527746	+	1.52482i	0.822224	+	0.569165i	$0.192733\pi$
$211$	1617.52	+	4673.51i	0.527746	+	1.52482i	−0.294477	+	0.955659i	$0.595146\pi$
$212$	−1016.51	+	524.045i	−0.329311	+	0.169772i
$213$	−842.157	+	3478.32i	−0.270909	+	1.11892i
$214$	1064.28	−	836.960i	0.339966	−	0.267352i
$215$	−1686.61	−	495.235i	−0.535005	−	0.157092i
$216$	−1361.48	+	1575.57i	−0.428875	+	0.496315i
$217$	596.006	−	4145.31i	0.186449	−	1.29678i
$218$	−5763.24	+	550.322i	−1.79053	+	0.170975i
$219$	−2723.01	+	526.102i	−0.840202	+	0.162332i
$220$	−263.844	−	207.489i	−0.0808560	−	0.0635859i
$221$	42.2964	+	887.912i	0.0128741	+	0.270260i
$222$	−4312.85	+	4981.87i	−1.30387	+	1.50613i
$223$	224.315	−	176.403i	0.0673599	−	0.0529724i	−0.583911	−	0.811817i	$-0.698478\pi$
$223$	224.315	−	176.403i	0.0673599	−	0.0529724i	0.651271	+	0.758845i	$0.274236\pi$
$224$	1536.99	+	1773.78i	0.458457	+	0.529087i
$225$	2273.41	+	907.738i	0.673602	+	0.268959i
$226$	−1409.88	+	1627.08i	−0.414972	+	0.478903i
$227$	−1650.39	−	1573.64i	−0.482555	−	0.460116i	0.409324	−	0.912389i	$-0.365765\pi$
$227$	−1650.39	−	1573.64i	−0.482555	−	0.460116i	−0.891879	+	0.452274i	$0.850613\pi$
$228$	−1306.77	−	2261.01i	−0.379574	−	0.656751i
$229$	−1327.93	+	2300.05i	−0.383198	+	0.663719i	−0.991517	−	0.129974i	$-0.958511\pi$
$229$	−1327.93	+	2300.05i	−0.383198	+	0.663719i	0.608319	+	0.793692i	$0.291844\pi$
$230$	5182.24	−	1928.39i	1.48568	−	0.552845i
$231$	−493.620	+	47.3615i	−0.140597	+	0.0134899i
$232$	−1395.78	+	1960.10i	−0.394989	+	0.554684i
$233$	60.9270	−	17.8898i	0.0171307	−	0.00503003i	−0.273156	−	0.961970i	$-0.588068\pi$
$233$	60.9270	−	17.8898i	0.0171307	−	0.00503003i	0.290287	+	0.956940i	$0.406249\pi$
$234$	2367.42	+	4091.89i	0.661381	+	1.14314i
$235$	−4408.74	−	2833.33i	−1.22381	−	0.786493i
$236$	−991.501	+	2864.75i	−0.273480	+	0.790168i
$237$	4066.41	+	1192.00i	1.11452	+	0.326703i
$238$	652.810	−	622.453i	0.177796	−	0.169528i
$239$	−189.889	−	3986.27i	−0.0513930	−	1.07887i	−0.866378	−	0.499389i	$-0.833558\pi$
$239$	−189.889	−	3986.27i	−0.0513930	−	1.07887i	0.814985	−	0.579482i	$-0.196745\pi$
$240$	−5416.54	+	2795.54i	−1.45682	+	0.751880i
$241$	−2278.90	+	217.608i	−0.609115	+	0.0581634i	−0.395056	−	0.918657i	$-0.629275\pi$
$241$	−2278.90	+	217.608i	−0.609115	+	0.0581634i	−0.214059	+	0.976821i	$0.568669\pi$
$242$	1831.83	−	4011.14i	0.486588	−	1.06548i
$243$	3721.16	+	708.425i	0.982356	+	0.187018i
$244$	−4.04570	+	2.60002i	−0.00106147	+	0.000682168i
$245$	382.587	+	1577.05i	0.0997658	+	0.411240i
$246$	4991.19	−	4763.42i	1.29360	−	1.23457i
$247$	6931.58	−	1335.95i	1.78561	−	0.344148i
$248$	−3623.39	+	1867.99i	−0.927763	+	0.478295i
$249$	−201.314	−	440.287i	−0.0512361	−	0.112056i
$250$	−1245.70	−	1187.77i	−0.315140	−	0.300485i
$251$	1235.45	+	2705.26i	0.310681	+	0.680296i	0.998981	−	0.0451301i	$-0.0143702\pi$
$251$	1235.45	+	2705.26i	0.310681	+	0.680296i	−0.688301	+	0.725426i	$0.741643\pi$
$252$	490.435	−	1421.20i	0.122597	−	0.355266i
$253$	−386.525	−	572.026i	−0.0960498	−	0.142146i
$254$	1763.46	+	3054.41i	0.435628	+	0.754530i
$255$	661.735	+	1144.96i	0.162508	+	0.281176i
$256$	1088.80	−	4488.08i	0.265820	−	1.09572i
$257$	1099.79	+	3177.65i	0.266939	+	0.771269i	0.996205	+	0.0870390i	$0.0277405\pi$
$257$	1099.79	+	3177.65i	0.266939	+	0.771269i	−0.729266	+	0.684230i	$0.760138\pi$
$258$	−1887.50	−	971.989i	−0.455468	−	0.234548i
$259$	−1852.72	+	5353.10i	−0.444489	+	1.28427i
$260$	391.483	+	2722.83i	0.0933799	+	0.649471i
$261$	4357.87	+	412.128i	1.03351	+	0.0977397i
$262$	−2986.61	+	1919.38i	−0.704250	+	0.452594i
$263$	−5194.44	+	2079.54i	−1.21788	+	0.487566i	−0.889481	−	0.456972i	$-0.848934\pi$
$263$	−5194.44	+	2079.54i	−1.21788	+	0.487566i	−0.328401	+	0.944538i	$0.606510\pi$
$264$	316.266	+	364.655i	0.0737304	+	0.0850113i
$265$	−2667.69	−	3746.24i	−0.618395	−	0.868415i
$266$	−5630.53	−	4427.90i	−1.29786	−	1.02065i
$267$	−2595.97	−	1037.90i	−0.595021	−	0.237897i
$268$	−105.321	−	434.138i	−0.0240055	−	0.0989522i
$269$	487.982	+	3393.99i	0.110605	+	0.769275i	0.967333	+	0.253507i	$0.0815842\pi$
$269$	487.982	+	3393.99i	0.110605	+	0.769275i	−0.856728	+	0.515768i	$0.827507\pi$
$270$	5921.60	+	3794.18i	1.33473	+	0.855209i
$271$	−3027.61	−	1945.73i	−0.678651	−	0.436142i	0.155384	−	0.987854i	$-0.450338\pi$
$271$	−3027.61	−	1945.73i	−0.678651	−	0.436142i	−0.834035	+	0.551712i	$0.813975\pi$
$272$	−1359.29	−	261.982i	−0.303012	−	0.0584007i
$273$	3195.65	+	2510.73i	0.708459	+	0.556617i
$274$	−1866.82	−	178.260i	−0.411601	−	0.0393032i
$275$	283.725	−	491.426i	0.0622155	−	0.107760i
$276$	2064.21	−	346.466i	0.450184	−	0.0755609i
$277$	2227.92	+	3858.87i	0.483259	+	0.837029i	0.999815	−	0.0192245i	$-0.00611971\pi$
$277$	2227.92	+	3858.87i	0.483259	+	0.837029i	−0.516556	+	0.856253i	$0.672786\pi$
$278$	3861.90	+	8456.38i	0.833171	+	1.82439i
$279$	6242.17	+	4003.59i	1.33946	+	0.859098i
$280$	−2176.45	+	2511.76i	−0.464527	+	0.536093i
$281$	12.8626	−	270.019i	0.00273067	−	0.0573238i	−0.997091	−	0.0762242i	$-0.975714\pi$
$281$	12.8626	−	270.019i	0.00273067	−	0.0573238i	0.999821	+	0.0189004i	$0.00601655\pi$
$282$	−4582.95	−	4365.86i	−0.967769	−	0.921926i
$283$	610.671	+	244.476i	0.128271	+	0.0513518i	0.434910	−	0.900474i	$-0.356780\pi$
$283$	610.671	+	244.476i	0.128271	+	0.0513518i	−0.306639	+	0.951826i	$0.599204\pi$
$284$	−1820.33	+	1735.68i	−0.380340	+	0.362654i
$285$	8251.99	−	6495.51i	1.71511	−	1.35004i
$286$	1017.35	−	407.286i	0.210340	−	0.0842074i
$287$	2463.91	−	5395.21i	0.506760	−	1.10965i
$288$	−3986.59	+	1174.51i	−0.815668	+	0.240308i
$289$	656.451	−	4565.72i	0.133615	−	0.929313i
$290$	7223.57	+	3724.01i	1.46270	+	0.754074i
$291$	−260.356	+	300.743i	−0.0524480	+	0.0605838i
$292$	−1809.50	−	724.416i	−0.362648	−	0.145182i
$293$	5643.82	−	1087.76i	1.12531	−	0.216885i	0.407554	−	0.913181i	$-0.366382\pi$
$293$	5643.82	−	1087.76i	1.12531	−	0.216885i	0.717755	+	0.696296i	$0.245170\pi$
$294$	94.1500	+	1957.72i	0.0186767	+	0.388356i
$295$	−11970.5	−	2307.12i	−2.36253	−	0.455341i
$296$	5290.63	−	1553.47i	1.03889	−	0.305046i
$297$	286.062	−	830.185i	0.0558889	−	0.162196i
$298$	−9582.05			−1.86266
$299$	−942.484	+	5578.81i	−0.182292	+	1.07903i
$300$	998.570	+	1400.95i	0.192175	+	0.269612i
$301$	−1816.87	−	173.490i	−0.347915	−	0.0332219i
$302$	509.007	−	2098.16i	0.0969870	−	0.399786i
$303$	−1972.22	−	4313.37i	−0.373931	−	0.817810i
$304$	−523.076	+	10980.7i	−0.0986857	+	2.07167i
$305$	−12.6646	−	14.6157i	−0.00237762	−	0.00274392i
$306$	523.769	+	1508.89i	0.0978493	+	0.281887i
$307$	3979.38	+	1168.45i	0.739789	+	0.217222i	0.629850	−	0.776717i	$-0.283116\pi$
$307$	3979.38	+	1168.45i	0.739789	+	0.217222i	0.109939	+	0.993938i	$0.464934\pi$
$308$	−309.767	−	159.696i	−0.0573073	−	0.0295439i
$309$	−228.462	+	4842.33i	−0.0420607	+	0.891490i
$310$	7986.36	+	11215.3i	1.46321	+	2.05479i
$311$	776.302	+	1090.16i	0.141544	+	0.198770i	0.879262	−	0.476338i	$-0.158036\pi$
$311$	776.302	+	1090.16i	0.141544	+	0.198770i	−0.737719	+	0.675108i	$0.764097\pi$
$312$	186.432	−	3951.50i	0.0338290	−	0.717017i
$313$	642.269	+	331.112i	0.115985	+	0.0597942i	0.515242	−	0.857044i	$-0.327702\pi$
$313$	642.269	+	331.112i	0.115985	+	0.0597942i	−0.399258	+	0.916839i	$0.630732\pi$
$314$	−4870.42	−	1430.09i	−0.875331	−	0.257020i
$315$	5937.69	+	1138.80i	1.06207	+	0.203695i
$316$	1950.26	+	2250.72i	0.347185	+	0.400673i
$317$	26.8430	−	563.504i	0.00475600	−	0.0998408i	−0.995241	−	0.0974428i	$-0.968934\pi$
$317$	26.8430	−	563.504i	0.00475600	−	0.0998408i	0.999997	−	0.00239794i	$-0.000763288\pi$
$318$	−2309.77	−	5051.61i	−0.407313	−	0.890819i
$319$	239.224	−	986.094i	0.0419874	−	0.173074i
$320$	1660.81	+	158.588i	0.290132	+	0.0277042i
$321$	1196.29	+	1678.34i	0.208007	+	0.291825i
$322$	4904.52	−	2984.35i	0.848814	−	0.516495i
$323$	2385.02			0.410855
$324$	1930.06	+	1833.62i	0.330944	+	0.314407i
$325$	−4462.09	+	1310.19i	−0.761576	+	0.223619i
$326$	−6886.74	−	1327.31i	−1.17000	−	0.225500i
$327$	−423.340	−	8802.79i	−0.0715925	−	1.48867i
$328$	−5669.12	+	1092.63i	−0.954344	+	0.183935i
$329$	−5051.58	−	2022.35i	−0.846513	−	0.338893i
$330$	1067.04	−	1232.56i	0.177996	−	0.205607i
$331$	6571.52	+	3387.86i	1.09125	+	0.562578i	0.907354	−	0.420368i	$-0.138099\pi$
$331$	6571.52	+	3387.86i	1.09125	+	0.562578i	0.183895	+	0.982946i	$0.441129\pi$
$332$	48.4219	−	336.782i	0.00800451	−	0.0556726i
$333$	−7265.79	−	6915.32i	−1.19568	−	1.13801i
$334$	286.749	−	627.893i	0.0469767	−	0.102865i
$335$	1667.79	−	667.682i	0.272003	−	0.108894i
$336$	−4973.00	+	3914.47i	−0.807439	+	0.635572i
$337$	3561.06	−	3395.46i	0.575618	−	0.548850i	−0.345358	−	0.938471i	$-0.612242\pi$
$337$	3561.06	−	3395.46i	0.575618	−	0.548850i	0.920975	+	0.389621i	$0.127394\pi$
$338$	−1375.34	−	550.605i	−0.221328	−	0.0886064i
$339$	−2372.92	−	2260.52i	−0.380176	−	0.362167i
$340$	−44.2227	+	928.349i	−0.00705386	+	0.148079i
$341$	1125.73	−	1299.16i	0.178773	−	0.206315i
$342$	11268.6	−	5822.35i	1.78169	−	0.920574i
$343$	2872.57	+	6290.06i	0.452199	+	0.990178i
$344$	888.294	+	1538.57i	0.139226	+	0.241146i
$345$	2560.45	+	8018.21i	0.399565	+	1.25126i
$346$	−5856.01	+	10142.9i	−0.909887	+	1.57597i
$347$	−2763.93	−	263.924i	−0.427596	−	0.0408305i	−0.120960	−	0.992657i	$-0.538597\pi$
$347$	−2763.93	−	263.924i	−0.427596	−	0.0408305i	−0.306636	+	0.951827i	$0.599203\pi$
$348$	2419.06	+	1900.59i	0.372630	+	0.292765i
$349$	−1856.97	−	357.901i	−0.284817	−	0.0548940i	0.0448419	−	0.998994i	$-0.485722\pi$
$349$	−1856.97	−	357.901i	−0.284817	−	0.0548940i	−0.329659	+	0.944100i	$0.606934\pi$
$350$	3969.80	+	2551.24i	0.606271	+	0.389627i
$351$	−6391.78	+	3306.24i	−0.971989	+	0.502774i
$352$	137.106	+	953.590i	0.0207607	+	0.144394i
$353$	1634.16	+	6736.09i	0.246395	+	1.01565i	0.951768	+	0.306818i	$0.0992643\pi$
$353$	1634.16	+	6736.09i	0.246395	+	1.01565i	−0.705373	+	0.708836i	$0.749221\pi$
$354$	−13671.6	−	5466.08i	−2.05265	−	0.820676i
$355$	−7950.58	−	6252.40i	−1.18866	−	0.934769i
$356$	−1139.73	−	1600.53i	−0.169679	−	0.238280i
$357$	899.640	+	1037.29i	0.133372	+	0.153779i
$358$	6583.19	−	2635.51i	0.971878	−	0.389081i
$359$	−2283.75	+	1467.68i	−0.335743	+	0.215769i	−0.697639	−	0.716450i	$-0.745766\pi$
$359$	−2283.75	+	1467.68i	−0.335743	+	0.215769i	0.361896	+	0.932219i	$0.382130\pi$
$360$	−2449.63	−	5351.06i	−0.358630	−	0.783404i
$361$	−1719.32	−	11958.1i	−0.250667	−	1.74342i
$362$	4205.28	−	12150.4i	0.610566	−	1.76411i
$363$	5967.73	+	3073.15i	0.862878	+	0.444348i
$364$	934.159	+	2699.08i	0.134514	+	0.388654i
$365$	1847.92	−	7617.23i	0.264999	−	1.09234i
$366$	−11.6881	−	20.2232i	−0.00166926	−	0.00288821i
$367$	−3375.54	−	5846.61i	−0.480114	−	0.831582i	0.519626	−	0.854394i	$-0.326071\pi$
$367$	−3375.54	−	5846.61i	−0.480114	−	0.831582i	−0.999740	+	0.0228123i	$0.992738\pi$
$368$	−8096.93	−	3474.59i	−1.14696	−	0.492189i
$369$	6884.97	+	7931.09i	0.971320	+	1.11891i
$370$	−7736.29	−	16940.1i	−1.08700	−	2.38020i
$371$	−3455.92	−	3295.21i	−0.483618	−	0.461129i
$372$	2167.21	+	4739.82i	0.302055	+	0.660614i
$373$	6369.87	−	3283.90i	0.884235	−	0.455855i	0.0445991	−	0.999005i	$-0.485799\pi$
$373$	6369.87	−	3283.90i	0.884235	−	0.455855i	0.839635	+	0.543150i	$0.182769\pi$
$374$	363.556	−	70.0696i	0.0502647	−	0.00968774i
$375$	1895.44	−	1808.94i	0.261013	−	0.249102i
$376$	1248.73	+	5147.34i	0.171272	+	0.705994i
$377$	−6995.71	+	4495.87i	−0.955696	+	0.614189i
$378$	6782.80	+	2704.69i	0.922935	+	0.368028i
$379$	−1229.48	+	2692.18i	−0.166634	+	0.364877i	−0.974466	−	0.224536i	$-0.927913\pi$
$379$	−1229.48	+	2692.18i	−0.166634	+	0.364877i	0.807832	+	0.589412i	$0.200641\pi$
$380$	7347.21	−	701.574i	0.991853	−	0.0947105i
$381$	−4770.90	+	2462.32i	−0.641524	+	0.331098i
$382$	−157.753	−	3311.64i	−0.0211291	−	0.443555i
$383$	−2368.55	+	2258.41i	−0.315998	+	0.301304i	−0.831433	−	0.555625i	$-0.812479\pi$
$383$	−2368.55	+	2258.41i	−0.315998	+	0.301304i	0.515435	+	0.856929i	$0.327630\pi$
$384$	8073.89	+	2366.72i	1.07297	+	0.314521i
$385$	458.383	−	1324.41i	0.0606788	−	0.175320i
$386$	11888.3	+	7640.15i	1.56761	+	1.00744i
$387$	1613.37	−	2800.32i	0.211918	−	0.367825i
$388$	−268.238	+	78.7618i	−0.0350972	+	0.0103055i
$389$	5027.57	−	7060.24i	0.655291	−	0.920227i	−0.344537	−	0.938773i	$-0.611964\pi$
$389$	5027.57	−	7060.24i	0.655291	−	0.920227i	0.999828	+	0.0185454i	$0.00590352\pi$
$390$	−13299.6	+	1276.06i	−1.72680	+	0.165682i
$391$	−669.391	+	1790.55i	−0.0865794	+	0.231591i
$392$	820.059	−	1420.38i	0.105661	−	0.183011i
$393$	−2704.26	−	4679.00i	−0.347104	−	0.600571i
$394$	1529.49	+	1458.37i	0.195570	+	0.186476i
$395$	−7842.74	+	9051.00i	−0.999015	+	1.15293i
$396$	484.742	−	381.919i	0.0615131	−	0.0484650i
$397$	5461.07	+	6302.41i	0.690386	+	0.796747i	0.987420	−	0.158119i	$-0.0505431\pi$
$397$	5461.07	+	6302.41i	0.690386	+	0.796747i	−0.297034	+	0.954867i	$0.595998\pi$
$398$	−8300.03	+	6527.22i	−1.04533	+	0.822060i
$399$	7136.79	−	8243.87i	0.895455	−	1.03436i
$400$	−344.595	−	7233.94i	−0.0430744	−	0.904243i
$401$	−4407.97	−	3466.47i	−0.548936	−	0.431688i	0.304783	−	0.952422i	$-0.401416\pi$
$401$	−4407.97	−	3466.47i	−0.548936	−	0.431688i	−0.853719	+	0.520733i	$0.825659\pi$
$402$	2130.36	−	411.598i	0.264310	−	0.0510663i
$403$	−14024.3	+	1339.16i	−1.73350	+	0.165529i
$404$	474.376	−	3299.35i	0.0584185	−	0.406310i
$405$	−6194.07	+	8731.91i	−0.759964	+	1.07134i
$406$	8096.41	+	2377.32i	0.989699	+	0.290602i
$407$	−1827.71	+	1437.33i	−0.222596	+	0.175051i
$408$	314.513	−	1299.02i	0.0381635	−	0.157625i
$409$	−3649.56	+	1881.48i	−0.441220	+	0.227465i	−0.664498	−	0.747290i	$-0.731355\pi$
$409$	−3649.56	+	1881.48i	−0.441220	+	0.227465i	0.223278	+	0.974755i	$0.428324\pi$
$410$	6377.62	+	18426.9i	0.768215	+	2.21961i
$411$	404.979	−	2825.81i	0.0486037	−	0.339141i
$412$	−1976.24	+	2775.24i	−0.236316	+	0.331859i
$413$	−12657.6			−1.50808
$414$	1208.41	+	10094.0i	0.143455	+	1.19829i
$415$	1368.26			0.161844
$416$	4579.77	−	6431.39i	0.539764	−	0.757993i
$417$	−13135.4	+	5265.57i	−1.54255	+	0.618359i
$418$	−961.655	−	2778.52i	−0.112526	−	0.325124i
$419$	−5086.41	+	2622.22i	−0.593048	+	0.305738i	−0.728499	−	0.685046i	$-0.759782\pi$
$419$	−5086.41	+	2622.22i	−0.593048	+	0.305738i	0.135451	+	0.990784i	$0.456752\pi$
$420$	3076.52	+	2930.79i	0.357426	+	0.340495i
$421$	8003.19	−	6293.78i	0.926489	−	0.728599i	−0.0361616	−	0.999346i	$-0.511513\pi$
$421$	8003.19	−	6293.78i	0.926489	−	0.728599i	0.962651	+	0.270747i	$0.0872707\pi$
$422$	−16197.6	−	4756.04i	−1.86845	−	0.548627i
$423$	6967.30	−	6655.41i	0.800855	−	0.765006i
$424$	−661.496	+	4600.81i	−0.0757667	+	0.526969i
$425$	−1564.10	+	149.354i	−0.178518	+	0.0170464i
$426$	−8004.12	−	9228.77i	−0.910331	−	1.04961i
$427$	−15.7839	−	12.4126i	−0.00178885	−	0.00140676i
$428$	68.9226	+	1446.86i	0.00778388	+	0.163404i
$429$	546.315	+	1576.15i	0.0614833	+	0.177383i
$430$	4716.54	−	3709.13i	0.528958	−	0.415977i
$431$	9741.97	+	11242.8i	1.08876	+	1.25649i	0.964455	+	0.264247i	$0.0851235\pi$
$431$	9741.97	+	11242.8i	1.08876	+	1.25649i	0.124301	+	0.992245i	$0.460331\pi$
$432$	−2656.93	−	10887.2i	−0.295906	−	1.21252i
$433$	−4391.98	+	5068.62i	−0.487449	+	0.562546i	−0.945182	−	0.326544i	$-0.894116\pi$
$433$	−4391.98	+	5068.62i	−0.487449	+	0.562546i	0.457733	+	0.889090i	$0.348661\pi$
$434$	10346.1	+	9864.99i	1.14431	+	1.09109i
$435$	−6180.77	+	10716.7i	−0.681254	+	1.18121i
$436$	3096.87	−	5363.94i	0.340168	−	0.589188i
$437$	14831.0	+	3238.10i	1.62349	+	0.354461i
$438$	3928.75	−	8613.13i	0.428592	−	0.939615i
$439$	7215.20	−	10132.3i	0.784425	−	1.10157i	−0.207929	−	0.978144i	$-0.566672\pi$
$439$	7215.20	−	10132.3i	0.784425	−	1.10157i	0.992354	−	0.123427i	$-0.0393884\pi$
$440$	−1308.96	+	384.344i	−0.141823	+	0.0416429i
$441$	−2983.58	+	2.71313i	−0.322166	+	0.000292963i
$442$	−2552.62	−	1640.47i	−0.274696	−	0.176537i
$443$	1222.94	−	3533.45i	0.131159	−	0.378960i	−0.860230	−	0.509906i	$-0.829680\pi$
$443$	1222.94	−	3533.45i	0.131159	−	0.378960i	0.991389	+	0.130946i	$0.0418015\pi$
$444$	−1665.10	−	6850.04i	−0.177978	−	0.732182i
$445$	5718.56	−	5452.63i	0.609181	−	0.580853i
$446$	46.3496	+	972.998i	0.00492089	+	0.103302i
$447$	687.415	−	14570.0i	0.0727374	−	1.54170i
$448$	1724.41	−	164.661i	0.181854	−	0.0173649i
$449$	5098.18	−	11163.5i	0.535853	−	1.17335i	−0.427229	−	0.904144i	$-0.640510\pi$
$449$	5098.18	−	11163.5i	0.535853	−	1.17335i	0.963081	−	0.269210i	$-0.0867626\pi$
$450$	−7025.38	+	4523.97i	−0.735955	+	0.473915i
$451$	2048.11	−	1316.24i	0.213840	−	0.137426i
$452$	−543.020	−	2238.36i	−0.0565078	−	0.232928i
$453$	3153.84	+	924.494i	0.327109	+	0.0958864i
$454$	7643.36	−	1473.14i	0.790134	−	0.152286i
$455$	−10208.9	+	5263.07i	−1.05187	+	0.542278i
$456$	−10566.3	−	1004.11i	−1.08511	−	0.103118i
$457$	4598.75	+	4384.90i	0.470723	+	0.448833i	0.887930	−	0.459978i	$-0.152143\pi$
$457$	4598.75	+	4384.90i	0.470723	+	0.448833i	−0.417207	+	0.908811i	$0.636991\pi$
$458$	−3766.05	−	8246.50i	−0.384227	−	0.841340i
$459$	−2331.92	+	688.171i	−0.237135	+	0.0699805i
$460$	−1535.40	+	5712.80i	−0.155626	+	0.579045i
$461$	9008.12	+	15602.5i	0.910087	+	1.57632i	0.813940	+	0.580949i	$0.197319\pi$
$461$	9008.12	+	15602.5i	0.910087	+	1.57632i	0.0961469	+	0.995367i	$0.469348\pi$
$462$	845.684	−	1466.31i	0.0851619	−	0.147660i
$463$	4120.64	−	16985.5i	0.413612	−	1.70493i	−0.259798	−	0.965663i	$-0.583656\pi$
$463$	4120.64	−	16985.5i	0.413612	−	1.70493i	0.673410	−	0.739269i	$-0.264829\pi$
$464$	−4235.59	−	12237.9i	−0.423776	−	1.22442i
$465$	−17626.4	+	11339.1i	−1.75785	+	1.13083i
$466$	−70.8930	+	204.832i	−0.00704732	+	0.0203619i
$467$	−2235.37	−	15547.3i	−0.221500	−	1.54057i	−0.732368	−	0.680909i	$-0.761585\pi$
$467$	−2235.37	−	15547.3i	−0.221500	−	1.54057i	0.510868	−	0.859659i	$-0.329324\pi$
$468$	−5035.06	−	476.170i	−0.497320	−	0.0470319i
$469$	1569.16	−	1008.44i	0.154493	−	0.0992866i
$470$	16607.5	−	6648.66i	1.62989	−	0.652510i
$471$	2523.93	−	7303.14i	0.246914	−	0.714461i
$472$	7146.84	+	10036.3i	0.696949	+	0.978728i
$473$	−588.883	−	463.103i	−0.0572450	−	0.0450180i
$474$	−11365.9	+	8946.65i	−1.10138	+	0.866948i
$475$	2941.68	+	12125.8i	0.284155	+	1.17130i
$476$	137.333	+	955.169i	0.0132240	+	0.0919750i
$477$	7846.95	−	3149.73i	0.753223	−	0.302340i
$478$	11460.0	+	7364.87i	1.09658	+	0.704731i
$479$	18594.0	+	3583.71i	1.77366	+	0.341845i	0.968080	−	0.250640i	$-0.0806411\pi$
$479$	18594.0	+	3583.71i	1.77366	+	0.341845i	0.805581	+	0.592485i	$0.201853\pi$
$480$	1666.32	−	11627.0i	0.158451	−	1.10562i
$481$	18969.4	+	1811.36i	1.79819	+	0.171707i
$482$	3907.18	−	6767.43i	0.369226	−	0.639519i
$483$	4186.01	+	7671.68i	0.394348	+	0.722720i
$484$	2358.78	+	4085.53i	0.221523	+	0.383690i
$485$	−467.021	−	1022.63i	−0.0437244	−	0.0957431i
$486$	−9337.75	+	8944.15i	−0.871541	+	0.834804i
$487$	7889.82	−	9105.34i	0.734131	−	0.847233i	−0.258799	−	0.965931i	$-0.583327\pi$
$487$	7889.82	−	9105.34i	0.734131	−	0.847233i	0.992930	+	0.118698i	$0.0378722\pi$
$488$	−0.930031	+	19.5238i	−8.62716e−5	+	0.00181106i
$489$	2512.30	−	10376.4i	0.232332	−	0.959589i
$490$	−5142.57	−	2058.77i	−0.474118	−	0.189808i
$491$	5229.83	−	4986.63i	0.480690	−	0.458337i	−0.410570	−	0.911829i	$-0.634670\pi$
$491$	5229.83	−	4986.63i	0.480690	−	0.458337i	0.891260	+	0.453492i	$0.149822\pi$
$492$	1053.78	+	7305.63i	0.0965612	+	0.669437i
$493$	−2608.35	+	1044.22i	−0.238284	+	0.0953946i
$494$	−10009.9	+	21918.7i	−0.911678	+	1.99630i
$495$	1797.63	+	1710.92i	0.163227	+	0.155354i
$496$	3122.29	−	21716.0i	0.282651	−	1.96588i
$497$	−9334.43	−	4812.23i	−0.842468	−	0.434322i
$498$	1622.84	+	312.012i	0.146027	+	0.0280755i
$499$	1628.01	+	651.758i	0.146052	+	0.0584704i	0.443537	−	0.896256i	$-0.353724\pi$
$499$	1628.01	+	651.758i	0.146052	+	0.0584704i	−0.297485	+	0.954727i	$0.596148\pi$
$500$	1808.13	−	348.489i	0.161724	−	0.0311698i
$501$	934.174	+	481.063i	0.0833050	+	0.0428988i
$502$	−9968.27	−	1921.23i	−0.886267	−	0.170814i
$503$	9721.77	−	2854.57i	0.861774	−	0.253040i	0.179161	−	0.983820i	$-0.442662\pi$
$503$	9721.77	−	2854.57i	0.861774	−	0.253040i	0.682613	+	0.730780i	$0.260843\pi$
$504$	−3548.94	−	4974.21i	−0.313656	−	0.439621i
$505$	13404.4			1.18117
$506$	2355.87	+	57.8717i	0.206978	+	0.00508440i
$507$	935.891	−	2051.78i	0.0819810	−	0.179730i
$508$	−3756.13	−	358.667i	−0.328054	−	0.0313254i
$509$	191.187	−	788.084i	0.0166488	−	0.0686271i	−0.962881	−	0.269925i	$-0.913001\pi$
$509$	191.187	−	788.084i	0.0166488	−	0.0686271i	0.979530	+	0.201298i	$0.0645161\pi$
$510$	−4493.84	−	427.048i	−0.390177	−	0.0370784i
$511$	387.237	−	8129.10i	0.0335232	−	0.703738i
$512$	1840.65	+	2124.22i	0.158879	+	0.183356i
$513$	8044.78	+	17552.2i	0.692370	+	1.51062i
$514$	−11013.2	−	3233.76i	−0.945079	−	0.277500i
$515$	−12177.7	−	6278.05i	−1.04197	−	0.537172i
$516$	2018.37	−	1041.70i	0.172197	−	0.0888728i
$517$	−1295.57	−	1819.38i	−0.110211	−	0.154770i
$518$	−11216.1	−	15750.8i	−0.951363	−	1.33600i
$519$	−15002.7	−	9632.02i	−1.26887	−	0.814641i
$520$	9937.40	+	5123.09i	0.838046	+	0.432043i
$521$	−15175.3	−	4455.87i	−1.27609	−	0.374694i	−0.427630	−	0.903954i	$-0.640651\pi$
$521$	−15175.3	−	4455.87i	−1.27609	−	0.374694i	−0.848459	+	0.529260i	$0.822469\pi$
$522$	−9774.58	+	11301.2i	−0.819582	+	0.947588i
$523$	9796.15	+	11305.4i	0.819036	+	0.945218i	0.999262	−	0.0384074i	$-0.0122285\pi$
$523$	9796.15	+	11305.4i	0.819036	+	0.945218i	−0.180226	+	0.983625i	$0.557683\pi$
$524$	180.721	−	3793.81i	0.0150665	−	0.316285i
$525$	−4164.08	+	5853.27i	−0.346163	+	0.486586i
$526$	4502.82	−	18560.9i	0.373255	−	1.53858i
$527$	−4738.29	−	452.452i	−0.391657	−	0.0373987i
$528$	−2585.92	+	248.112i	−0.213140	+	0.0204502i
$529$	−6593.53	+	10225.5i	−0.541919	+	0.840431i
$530$	15698.6			1.28661
$531$	9292.27	−	20396.3i	0.759417	−	1.66690i
$532$	7352.84	−	2158.99i	0.599222	−	0.175947i
$533$	−19591.8	−	3776.01i	−1.59215	−	0.306862i
$534$	8025.97	−	5163.14i	0.650408	−	0.418410i
$535$	−5719.73	+	1102.39i	−0.462216	+	0.0890848i
$536$	−1685.60	−	674.812i	−0.135834	−	0.0543795i
$537$	3535.16	+	10199.2i	0.284084	+	0.819602i
$538$	−10403.3	−	5363.29i	−0.833679	−	0.429791i
$539$	−98.4274	+	684.578i	−0.00786562	+	0.0547066i
$540$	−6981.21	+	2805.91i	−0.556339	+	0.223606i
$541$	1364.58	−	2988.01i	0.108443	−	0.237458i	−0.847629	−	0.530590i	$-0.821970\pi$
$541$	1364.58	−	2988.01i	0.108443	−	0.237458i	0.956072	+	0.293132i	$0.0946977\pi$
$542$	11404.9	−	4565.83i	0.903841	−	0.361843i
$543$	18173.6	+	7266.02i	1.43629	+	0.574245i
$544$	1930.60	−	1840.83i	0.152158	−	0.145082i
$545$	23123.3	+	9257.16i	1.81742	+	0.727584i
$546$	−13308.6	+	3914.33i	−1.04314	+	0.306810i
$547$	467.675	−	9817.71i	0.0365564	−	0.767413i	−0.903950	−	0.427638i	$-0.859346\pi$
$547$	467.675	−	9817.71i	0.0365564	−	0.767413i	0.940507	−	0.339775i	$-0.110351\pi$
$548$	1313.83	−	1516.24i	0.102416	−	0.118194i
$549$	31.5890	−	16.3216i	0.00245571	−	0.00126883i
$550$	804.651	+	1761.94i	0.0623826	+	0.136599i
$551$	11155.9	+	19322.6i	0.862538	+	1.49396i
$552$	3719.41	−	7650.79i	0.286791	−	0.589927i
$553$	−6217.40	+	10768.8i	−0.478102	+	0.828098i
$554$	−15141.0	−	1445.79i	−1.16116	−	0.110877i
$555$	26313.3	−	10548.2i	2.01250	−	0.806746i
$556$	−9765.95	−	1882.23i	−0.744908	−	0.143569i
$557$	−12043.4	−	7739.79i	−0.916146	−	0.588771i	−0.00460880	−	0.999989i	$-0.501467\pi$
$557$	−12043.4	−	7739.79i	−0.916146	−	0.588771i	−0.911537	+	0.411218i	$0.865103\pi$
$558$	−23491.7	+	9429.46i	−1.78223	+	0.715378i
$559$	873.768	+	6077.19i	0.0661117	+	0.459817i
$560$	−4216.94	−	17382.5i	−0.318211	−	1.31168i
$561$	80.4631	+	557.832i	0.00605553	+	0.0419816i
$562$	725.331	+	570.406i	0.0544417	+	0.0428134i
$563$	5659.81	+	7948.09i	0.423681	+	0.594977i	0.970151	−	0.242502i	$-0.0779680\pi$
$563$	5659.81	+	7948.09i	0.423681	+	0.594977i	−0.546470	+	0.837479i	$0.684029\pi$
$564$	6648.68	−	1284.56i	0.496383	−	0.0959041i
$565$	8598.92	−	3442.49i	0.640282	−	0.256330i
$566$	−1888.91	+	1213.93i	−0.140277	+	0.0901506i
$567$	−4599.23	+	10119.6i	−0.340651	+	0.749527i
$568$	1454.82	+	10118.5i	0.107470	+	0.747470i
$569$	2316.36	−	6692.67i	0.170662	−	0.493095i	−0.826941	−	0.562288i	$-0.809921\pi$
$569$	2316.36	−	6692.67i	0.170662	−	0.493095i	0.997603	+	0.0691928i	$0.0220424\pi$
$570$	1721.98	+	35806.2i	0.126536	+	2.63115i
$571$	396.691	+	1146.16i	0.0290735	+	0.0840025i	0.958604	−	0.284744i	$-0.0919084\pi$
$571$	396.691	+	1146.16i	0.0290735	+	0.0840025i	−0.929530	+	0.368746i	$0.879787\pi$
$572$	−276.398	+	1139.33i	−0.0202041	+	0.0832826i
$573$	5046.84	−	2.29468i	0.367949	−	0.000167298i
$574$	10123.0	+	17533.6i	0.736110	+	1.27498i
$575$	−9929.00	−	1194.81i	−0.720118	−	0.0866559i
$576$	−1000.60	+	2899.58i	−0.0723814	+	0.209749i
$577$	5483.45	+	12007.1i	0.395631	+	0.866311i	0.997695	+	0.0678630i	$0.0216181\pi$
$577$	5483.45	+	12007.1i	0.395631	+	0.866311i	−0.602064	+	0.798448i	$0.705655\pi$
$578$	11395.4	+	10865.5i	0.820043	+	0.781910i
$579$	−12470.1	+	17528.7i	−0.895061	+	1.25815i
$580$	−7728.01	+	3984.07i	−0.553256	+	0.285223i
$581$	1394.98	−	268.860i	0.0996100	−	0.0191983i
$582$	−320.720	−	1319.41i	−0.0228424	−	0.0939711i
$583$	−462.100	−	1904.80i	−0.0328271	−	0.135315i
$584$	−6664.30	+	4282.89i	−0.472210	+	0.303471i
$585$	−986.206	−	20314.3i	−0.0697002	−	1.43572i
$586$	−8150.28	+	17846.6i	−0.574548	+	1.25808i
$587$	−11577.7	+	1105.54i	−0.814080	+	0.0777352i	−0.493786	−	0.869583i	$-0.664388\pi$
$587$	−11577.7	+	1105.54i	−0.814080	+	0.0777352i	−0.320293	+	0.947318i	$0.603781\pi$
$588$	−1764.50	−	1132.84i	−0.123753	−	0.0794519i
$589$	1798.56	+	37756.4i	0.125821	+	2.64130i
$590$	30116.7	−	28716.2i	2.10150	−	2.00378i
$591$	−2327.25	+	2221.05i	−0.161980	+	0.154588i
$592$	−9705.85	+	28043.2i	−0.673831	+	1.94691i
$593$	−8821.36	−	5669.14i	−0.610877	−	0.392586i	0.198309	−	0.980140i	$-0.436455\pi$
$593$	−8821.36	−	5669.14i	−0.610877	−	0.392586i	−0.809186	+	0.587553i	$0.800091\pi$
$594$	1741.95	+	2439.18i	0.120325	+	0.168486i
$595$	−3723.41	+	1093.29i	−0.256546	+	0.0753287i
$596$	5946.27	−	8350.37i	0.408672	−	0.573900i
$597$	−9329.53	−	13088.9i	−0.639585	−	0.897308i
$598$	−13646.0	−	13666.7i	−0.933153	−	0.934573i
$599$	8141.18	−	14100.9i	0.555325	−	0.961851i	−0.442553	−	0.896742i	$-0.645927\pi$
$599$	8141.18	−	14100.9i	0.555325	−	0.961851i	0.997878	−	0.0651090i	$-0.0207395\pi$
$600$	6992.29	−	3.17923i	0.475765	−	0.000216319i
$601$	−18748.5	−	17876.7i	−1.27249	−	1.21332i	−0.965144	−	0.261721i	$-0.915710\pi$
$601$	−18748.5	−	17876.7i	−1.27249	−	1.21332i	−0.307348	−	0.951597i	$-0.599441\pi$
$602$	4079.81	−	4708.36i	0.276214	−	0.318768i
$603$	473.025	+	3268.86i	0.0319454	+	0.220760i
$604$	1512.59	+	1745.62i	0.101898	+	0.117596i
$605$	−14912.3	+	11727.2i	−1.00210	+	0.788062i
$606$	15898.5	+	3056.69i	1.06573	+	0.204900i
$607$	595.427	+	12499.6i	0.0398149	+	0.835817i	0.927150	+	0.374691i	$0.122251\pi$
$607$	595.427	+	12499.6i	0.0398149	+	0.835817i	−0.887335	+	0.461126i	$0.847446\pi$
$608$	−16651.6	−	13095.0i	−1.11071	−	0.873471i
$609$	−4195.68	+	12140.5i	−0.279175	+	0.807810i
$610$	65.7158	−	6.27509i	0.00436189	−	0.000416510i
$611$	−2605.01	+	18118.3i	−0.172484	+	1.19965i
$612$	−1639.97	−	479.919i	−0.108320	−	0.0316987i
$613$	−2634.60	−	773.589i	−0.173590	−	0.0509706i	0.193783	−	0.981045i	$-0.437924\pi$
$613$	−2634.60	−	773.589i	−0.173590	−	0.0509706i	−0.367372	+	0.930074i	$0.619743\pi$
$614$	−11128.2	+	8751.27i	−0.731426	+	0.575200i
$615$	−28476.6	+	8375.56i	−1.86714	+	0.549163i
$616$	−1259.00	+	649.057i	−0.0823480	+	0.0424533i
$617$	6293.32	+	18183.4i	0.410631	+	1.18644i	0.940921	+	0.338625i	$0.109962\pi$
$617$	6293.32	+	18183.4i	0.410631	+	1.18644i	−0.530290	+	0.847816i	$0.677917\pi$
$618$	−13011.9	−	10223.1i	−0.846952	−	0.665428i
$619$	−1022.81	+	1436.34i	−0.0664139	+	0.0932653i	−0.846447	−	0.532473i	$-0.821263\pi$
$619$	−1022.81	+	1436.34i	−0.0664139	+	0.0932653i	0.780033	+	0.625738i	$0.215202\pi$
$620$	−14729.7			−0.954127
$621$	−15435.1	+	1113.31i	−0.997409	+	0.0719416i
$622$	−4568.33			−0.294491
$623$	4758.80	−	6682.80i	0.306031	−	0.429761i
$624$	16741.0	+	13152.9i	1.07400	+	0.843813i
$625$	6128.61	+	17707.5i	0.392231	+	1.13328i
$626$	−2192.37	+	1130.25i	−0.139976	+	0.0721625i
$627$	4293.87	−	1262.92i	0.273494	−	0.0804402i
$628$	4268.67	−	3356.92i	0.271240	−	0.213305i
$629$	6177.42	+	1813.85i	0.391589	+	0.114981i
$630$	−14923.2	+	14255.1i	−0.943736	+	0.901490i
$631$	−4276.84	+	29746.1i	−0.269823	+	1.87666i	0.180179	+	0.983634i	$0.442332\pi$
$631$	−4276.84	+	29746.1i	−0.269823	+	1.87666i	−0.450003	+	0.893027i	$0.648577\pi$
$632$	12049.3	−	1150.57i	0.758377	−	0.0724162i
$633$	8393.82	−	24288.1i	0.527053	−	1.52506i
$634$	1513.70	+	1190.38i	0.0948210	+	0.0745681i
$635$	−721.988	−	15156.4i	−0.0451200	−	0.947186i
$636$	5835.64	+	1121.98i	0.363834	+	0.0699516i
$637$	4455.40	−	3503.76i	0.277126	−	0.217934i
$638$	2268.21	+	2617.65i	0.140751	+	0.162435i
$639$	14607.0	−	11508.6i	0.904297	−	0.712479i
$640$	−15571.8	+	17970.8i	−0.961765	+	1.10994i
$641$	−9277.76	−	8846.33i	−0.571684	−	0.545100i	0.348134	−	0.937445i	$-0.386815\pi$
$641$	−9277.76	−	8846.33i	−0.571684	−	0.545100i	−0.919818	+	0.392345i	$0.871664\pi$
$642$	−7035.36	+	3.19881i	−0.432497	+	0.000196647i
$643$	5959.46	−	10322.1i	0.365503	−	0.633069i	−0.623354	−	0.781940i	$-0.714230\pi$
$643$	5959.46	−	10322.1i	0.365503	−	0.633069i	0.988857	+	0.148871i	$0.0475638\pi$
$644$	−442.825	+	6126.07i	−0.0270959	+	0.374846i
$645$	5301.56	+	7437.84i	0.323642	+	0.454054i
$646$	−4722.38	+	6631.65i	−0.287615	+	0.403899i
$647$	−13055.1	+	3833.31i	−0.793273	+	0.232926i	−0.653170	−	0.757211i	$-0.726561\pi$
$647$	−13055.1	+	3833.31i	−0.793273	+	0.232926i	−0.140103	+	0.990137i	$0.544743\pi$
$648$	10620.8	−	2067.03i	0.643863	−	0.125309i
$649$	−4370.80	−	2808.94i	−0.264359	−	0.169893i
$650$	5191.97	−	15001.2i	0.313301	−	0.905224i
$651$	−15742.5	+	15024.1i	−0.947767	+	0.904517i
$652$	5430.36	−	5177.84i	0.326180	−	0.311012i
$653$	704.835	+	14796.3i	0.0422394	+	0.886714i	0.916201	+	0.400719i	$0.131240\pi$
$653$	704.835	+	14796.3i	0.0422394	+	0.886714i	−0.873962	+	0.485995i	$0.838457\pi$
$654$	25314.7	+	16252.5i	1.51358	+	0.971749i
$655$	15204.5	−	1451.85i	0.907007	−	0.0866086i
$656$	12907.7	−	28263.8i	0.768231	−	1.68219i
$657$	12814.9	+	6591.78i	0.760968	+	0.391431i
$658$	15625.4	−	10041.9i	0.925749	−	0.594943i
$659$	−3515.18	−	14489.8i	−0.207788	−	0.856512i	−0.976255	−	0.216623i	$-0.930496\pi$
$659$	−3515.18	−	14489.8i	−0.207788	−	0.856512i	0.768468	−	0.639889i	$-0.221019\pi$
$660$	411.963	+	1694.77i	0.0242964	+	0.0999527i
$661$	−2766.41	+	533.182i	−0.162785	+	0.0313742i	−0.269992	−	0.962862i	$-0.587021\pi$
$661$	−2766.41	+	533.182i	−0.162785	+	0.0313742i	0.107208	+	0.994237i	$0.465809\pi$
$662$	−22431.8	+	11564.4i	−1.31697	+	0.678946i
$663$	2677.55	−	3763.71i	0.156844	−	0.220468i
$664$	−1000.83	−	954.287i	−0.0584934	−	0.0557734i
$665$	12801.8	+	28032.0i	0.746516	+	1.63464i
$666$	33614.7	−	6510.41i	1.95577	−	0.378788i
$667$	−17637.5	+	2952.10i	−1.02388	+	0.171373i
$668$	369.238	+	639.538i	0.0213866	+	0.0370426i
$669$	−1482.82	+	0.674204i	−0.0856938	+	3.89630e-5i
$670$	−1445.73	+	5959.38i	−0.0833633	+	0.343628i
$671$	−2.69578	−	7.78894i	−0.000155096	−	0.000448120i
$672$	−585.829	−	12181.5i	−0.0336292	−	0.699274i
$673$	−1296.50	+	3746.00i	−0.0742593	+	0.214558i	−0.976021	−	0.217675i	$-0.930153\pi$
$673$	−1296.50	+	3746.00i	−0.0742593	+	0.214558i	0.901762	+	0.432233i	$0.142274\pi$
$674$	2390.27	+	16624.7i	0.136602	+	0.950090i
$675$	−6374.93	−	11007.0i	−0.363513	−	0.627644i
$676$	1333.32	−	856.872i	0.0758602	−	0.0487524i
$677$	−30953.7	+	12392.0i	−1.75723	+	0.703490i	−0.758581	+	0.651578i	$0.774107\pi$
$677$	−30953.7	+	12392.0i	−1.75723	+	0.703490i	−0.998652	+	0.0519117i	$0.983469\pi$
$678$	10983.9	−	2122.15i	0.622173	−	0.120208i
$679$	−677.087	−	950.836i	−0.0382684	−	0.0537404i
$680$	2969.23	+	2335.03i	0.167448	+	0.131683i
$681$	1691.65	+	11727.8i	0.0951896	+	0.659928i
$682$	1383.41	+	5702.48i	0.0776735	+	0.320175i
$683$	−3673.46	−	25549.4i	−0.205799	−	1.43137i	−0.786672	−	0.617371i	$-0.788198\pi$
$683$	−3673.46	−	25549.4i	−0.205799	−	1.43137i	0.580873	−	0.813994i	$-0.302711\pi$
$684$	−1918.95	+	13433.3i	−0.107270	+	0.750927i
$685$	6787.22	+	4361.88i	0.378579	+	0.243298i
$686$	−23177.5	−	4467.09i	−1.28997	−	0.248622i
$687$	12809.4	−	5134.88i	0.711368	−	0.285164i
$688$	−9518.00	−	908.859i	−0.527428	−	0.0503632i
$689$	−8031.67	+	13911.3i	−0.444096	+	0.769198i
$690$	−27364.7	−	8756.75i	−1.50979	−	0.483136i
$691$	−12624.7	−	21866.6i	−0.695030	−	1.20383i	−0.970171	−	0.242424i	$-0.922058\pi$
$691$	−12624.7	−	21866.6i	−0.695030	−	1.20383i	0.275140	−	0.961404i	$-0.411276\pi$
$692$	−5205.11	−	11397.6i	−0.285937	−	0.626115i
$693$	2168.93	+	1391.10i	0.118890	+	0.0762533i
$694$	6206.48	−	7162.66i	0.339474	−	0.391773i
$695$	1903.06	−	39950.1i	0.103866	−	2.18042i
$696$	11995.3	−	3528.07i	0.653277	−	0.192142i
$697$	−6258.28	−	2505.44i	−0.340100	−	0.136155i
$698$	4671.97	−	4454.72i	0.253348	−	0.241567i
$699$	−306.372	−	122.491i	−0.0165780	−	0.00662810i
$700$	−4686.82	+	1876.32i	−0.253064	+	0.101312i
$701$	13288.4	−	29097.4i	0.715969	−	1.56775i	−0.103499	−	0.994630i	$-0.533004\pi$
$701$	13288.4	−	29097.4i	0.715969	−	1.56775i	0.819469	−	0.573124i	$-0.194269\pi$
$702$	3462.69	−	24319.0i	0.186169	−	1.30749i
$703$	7276.22	−	50607.2i	0.390367	−	2.71506i
$704$	631.998	+	325.818i	0.0338343	+	0.0174428i
$705$	8918.21	+	25729.6i	0.476424	+	1.37452i
$706$	−21965.6	−	8793.71i	−1.17094	−	0.468776i
$707$	13666.2	−	2633.94i	0.726973	−	0.140113i
$708$	13247.6	−	8522.22i	0.703213	−	0.452380i
$709$	−11246.7	−	2167.62i	−0.595738	−	0.114819i	−0.117536	−	0.993069i	$-0.537499\pi$
$709$	−11246.7	−	2167.62i	−0.595738	−	0.114819i	−0.478203	+	0.878250i	$0.658712\pi$
$710$	33127.3	−	9727.05i	1.75105	−	0.514155i
$711$	−12788.5	−	17924.4i	−0.674550	−	0.945452i
$712$	−7985.83			−0.420339
$713$	−28850.3	−	9246.61i	−1.51536	−	0.485678i
$714$	−4665.51	+	447.643i	−0.244541	+	0.0234631i
$715$	−4693.22	−	448.148i	−0.245478	−	0.0234403i
$716$	−1788.55	+	7372.49i	−0.0933535	+	0.384808i
$717$	−12020.8	+	16897.1i	−0.626116	+	0.880104i
$718$	440.921	−	9256.08i	0.0229179	−	0.481106i
$719$	5849.41	+	6750.58i	0.303402	+	0.350145i	0.886893	−	0.461975i	$-0.152859\pi$
$719$	5849.41	+	6750.58i	0.303402	+	0.350145i	−0.583491	+	0.812120i	$0.698314\pi$
$720$	31105.7	+	5965.80i	1.61006	+	0.308795i
$721$	−13649.2	−	4007.75i	−0.705022	−	0.207013i
$722$	36654.4	+	18896.7i	1.88938	+	0.974045i
$723$	10009.9	+	6426.57i	0.514901	+	0.330576i
$724$	7978.91	+	11204.8i	0.409577	+	0.575171i
$725$	−8526.10	−	11973.2i	−0.436761	−	0.613344i
$726$	−20361.2	+	10508.6i	−1.04087	+	0.537207i
$727$	−29409.1	−	15161.4i	−1.50031	−	0.773461i	−0.504367	−	0.863490i	$-0.668274\pi$
$727$	−29409.1	−	15161.4i	−1.50031	−	0.773461i	−0.995939	+	0.0900282i	$0.971304\pi$
$728$	11138.2	+	3270.46i	0.567043	+	0.166499i
$729$	−12930.2	−	14840.2i	−0.656920	−	0.753960i
$730$	17521.1	+	20220.4i	0.888336	+	1.02519i
$731$	−98.7025	+	2072.02i	−0.00499404	+	0.104838i
$732$	24.8769	+	2.36405i	0.00125612	+	0.000119368i
$733$	4524.68	−	18651.0i	0.227998	−	0.939822i	−0.736648	−	0.676276i	$-0.763593\pi$
$733$	4524.68	−	18651.0i	0.227998	−	0.939822i	0.964647	−	0.263546i	$-0.0848922\pi$
$734$	22940.3	+	2190.54i	1.15360	+	0.110156i
$735$	3499.40	−	7671.85i	0.175616	−	0.385008i
$736$	14504.5	−	8825.84i	0.726417	−	0.442017i
$737$	765.640			0.0382669
$738$	−35685.1	+	3440.26i	−1.77993	+	0.171596i
$739$	16115.5	−	4731.93i	0.802188	−	0.235544i	0.145159	−	0.989408i	$-0.453631\pi$
$739$	16115.5	−	4731.93i	0.802188	−	0.235544i	0.657030	+	0.753865i	$0.271813\pi$
$740$	19563.5	+	3770.55i	0.971849	+	0.187308i
$741$	−32610.5	−	16793.1i	−1.61670	−	0.832537i
$742$	16005.2	−	3084.75i	0.791873	−	0.152621i
$743$	−25512.4	−	10213.6i	−1.25970	−	0.504309i	−0.356811	−	0.934177i	$-0.616136\pi$
$743$	−25512.4	−	10213.6i	−1.25970	−	0.504309i	−0.902892	+	0.429868i	$0.858560\pi$
$744$	20801.4	+	3999.34i	1.02502	+	0.197074i
$745$	36641.3	+	18889.9i	1.80192	+	0.928957i
$746$	−3481.42	+	24213.8i	−0.170863	+	1.18838i
$747$	−590.853	+	2445.23i	−0.0289400	+	0.119768i
$748$	−164.547	+	360.307i	−0.00804334	+	0.0176125i
$749$	−5614.82	+	2247.83i	−0.273913	+	0.109658i
$750$	1276.84	+	8852.06i	0.0621649	+	0.430975i
$751$	−25438.9	+	24256.0i	−1.23606	+	1.17858i	−0.258937	+	0.965894i	$0.583372\pi$
$751$	−25438.9	+	24256.0i	−1.23606	+	1.17858i	−0.977121	+	0.212685i	$0.931779\pi$
$752$	−26463.7	−	10594.5i	−1.28329	−	0.513750i
$753$	3636.45	−	15019.5i	0.175989	−	0.726879i
$754$	1350.65	−	28353.7i	0.0652360	−	1.36947i
$755$	−6082.70	+	7019.81i	−0.293208	+	0.338380i
$756$	−6566.19	+	4232.50i	−0.315886	+	0.203617i
$757$	5577.63	+	12213.3i	0.267797	+	0.586394i	0.994983	−	0.100047i	$-0.0318993\pi$
$757$	5577.63	+	12213.3i	0.267797	+	0.586394i	−0.727186	+	0.686441i	$0.759172\pi$
$758$	−5051.34	−	8749.18i	−0.242049	−	0.419241i
$759$	−257.007	+	3578.07i	−0.0122908	+	0.171114i
$760$	14998.6	−	25978.4i	0.715866	−	1.23992i
$761$	−3238.12	−	309.203i	−0.154247	−	0.0147288i	0.0176470	−	0.999844i	$-0.494382\pi$
$761$	−3238.12	−	309.203i	−0.154247	−	0.0147288i	−0.171894	+	0.985116i	$0.554989\pi$
$762$	2599.88	−	18141.1i	0.123601	−	0.862444i
$763$	25393.9	+	4894.26i	1.20487	+	0.232221i
$764$	2983.85	+	1917.61i	0.141298	+	0.0908070i
$765$	971.736	−	6802.48i	0.0459258	−	0.321496i
$766$	−1589.83	−	11057.5i	−0.0749909	−	0.521573i
$767$	10038.5	+	41379.4i	0.472583	+	1.94801i
$768$	−18856.3	+	14842.7i	−0.885963	+	0.697381i
$769$	26255.4	+	20647.5i	1.23120	+	0.968229i	0.999989	−	0.00467434i	$-0.00148789\pi$
$769$	26255.4	+	20647.5i	1.23120	+	0.968229i	0.231214	+	0.972903i	$0.425730\pi$
$770$	2774.97	+	3896.90i	0.129874	+	0.182382i
$771$	5707.19	−	16514.1i	0.266588	−	0.771391i
$772$	−14035.5	+	5618.98i	−0.654339	+	0.261958i
$773$	19772.6	−	12707.1i	0.920012	−	0.591256i	0.00735126	−	0.999973i	$-0.497660\pi$
$773$	19772.6	−	12707.1i	0.920012	−	0.591256i	0.912661	+	0.408717i	$0.134024\pi$
$774$	4591.90	+	10030.7i	0.213246	+	0.465822i
$775$	−3543.87	−	24648.1i	−0.164257	−	1.14244i
$776$	−371.625	+	1073.74i	−0.0171914	+	0.0496714i
$777$	24754.5	−	15924.7i	1.14294	−	0.735257i
$778$	9676.61	+	27958.7i	0.445917	+	1.28839i
$779$	−12621.0	+	52024.4i	−0.580480	+	2.39277i
$780$	7141.22	−	12382.0i	0.327816	−	0.568392i
$781$	−2155.36	−	3733.19i	−0.0987514	−	0.171043i
$782$	−3653.29	−	5406.58i	−0.167060	−	0.247236i
$783$	−16482.9	−	15673.5i	−0.752299	−	0.715359i
$784$	3666.80	+	8029.17i	0.167037	+	0.365760i
$785$	15805.0	+	15070.1i	0.718606	+	0.685190i
$786$	18364.6	+	1745.18i	0.833389	+	0.0791966i
$787$	−25170.3	+	12976.2i	−1.14005	+	0.587739i	−0.921613	−	0.388111i	$-0.873128\pi$
$787$	−25170.3	+	12976.2i	−1.14005	+	0.587739i	−0.218442	+	0.975850i	$0.570097\pi$
$788$	−2220.05	+	427.880i	−0.100363	+	0.0193434i
$789$	27899.7	+	8178.33i	1.25888	+	0.369019i
$790$	−9637.95	−	39728.2i	−0.434054	−	1.78920i
$791$	8090.41	−	5199.39i	0.363669	−	0.233716i
$792$	−121.622	−	2505.22i	−0.00545663	−	0.112398i
$793$	−28.0606	+	61.4441i	−0.00125657	+	0.00275151i
$794$	−28337.1	+	2705.86i	−1.26656	+	0.120941i
$795$	−1126.22	+	23870.6i	−0.0502426	+	1.06491i
$796$	−537.509	−	11283.7i	−0.0239340	−	0.502437i
$797$	8115.29	−	7737.92i	0.360676	−	0.343903i	−0.487975	−	0.872858i	$-0.662264\pi$
$797$	8115.29	−	7737.92i	0.360676	−	0.343903i	0.848650	+	0.528954i	$0.177416\pi$
$798$	8791.46	+	36167.1i	0.389993	+	1.60439i
$799$	−2022.73	+	5844.29i	−0.0895608	+	0.258769i
$800$	11740.2	+	7544.96i	0.518848	+	0.333443i
$801$	7275.04	+	12574.3i	0.320913	+	0.554671i
$802$	18366.5	−	5392.89i	0.808657	−	0.237443i
$803$	1937.71	−	2721.13i	0.0851560	−	0.119585i
$804$	−963.334	+	2111.95i	−0.0422564	+	0.0926401i
$805$	−24638.0	+	1743.32i	−1.07873	+	0.0763280i
$806$	24044.7	−	41646.7i	1.05079	−	1.82003i
$807$	8901.50	−	15434.0i	0.388287	−	0.673239i
$808$	−9804.82	−	9348.88i	−0.426897	−	0.407045i
$809$	17192.4	−	19841.1i	0.747162	−	0.862271i	−0.247128	−	0.968983i	$-0.579487\pi$
$809$	17192.4	−	19841.1i	0.747162	−	0.862271i	0.994290	+	0.106712i	$0.0340322\pi$
$810$	−12015.1	−	34512.2i	−0.521195	−	1.49708i
$811$	−3420.49	−	3947.46i	−0.148101	−	0.170917i	0.676852	−	0.736119i	$-0.263344\pi$
$811$	−3420.49	−	3947.46i	−0.148101	−	0.170917i	−0.824953	+	0.565202i	$0.808798\pi$
$812$	−7096.07	+	5580.41i	−0.306679	+	0.241175i
$813$	6124.40	+	17669.3i	0.264197	+	0.762225i
$814$	−377.655	−	7927.96i	−0.0162614	−	0.341370i
$815$	23718.0	+	18652.0i	1.01939	+	0.801658i
$816$	4712.93	+	5434.02i	0.202188	+	0.233123i
$817$	16398.6	−	1565.87i	0.702219	−	0.0670538i
$818$	1994.65	−	13873.1i	0.0852582	−	0.592984i
$819$	−4997.19	−	20517.3i	−0.213206	−	0.875374i
$820$	−20016.0	−	5877.24i	−0.852427	−	0.250295i
$821$	−29815.4	+	23447.1i	−1.26744	+	0.996723i	−0.267992	+	0.963421i	$0.586360\pi$
$821$	−29815.4	+	23447.1i	−1.26744	+	0.996723i	−0.999445	+	0.0333022i	$0.989398\pi$
$822$	7055.42	+	6721.20i	0.299375	+	0.285193i
$823$	5159.18	−	2659.74i	0.218515	−	0.112652i	−0.345494	−	0.938421i	$-0.612289\pi$
$823$	5159.18	−	2659.74i	0.218515	−	0.112652i	0.564009	+	0.825769i	$0.309258\pi$
$824$	4528.92	+	13085.5i	0.191472	+	0.553221i
$825$	−2736.85	+	1097.11i	−0.115497	+	0.0462989i
$826$	25062.2	−	35194.9i	1.05572	−	1.48255i
$827$	26464.4			1.11277			0.556383	−	0.830926i	$-0.312189\pi$
$827$	26464.4			1.11277			0.556383	+	0.830926i	$0.312189\pi$
$828$	−9546.41	−	5210.88i	−0.400677	−	0.218709i
$829$	23208.0			0.972311			0.486156	−	0.873872i	$-0.338399\pi$
$829$	23208.0			0.972311			0.486156	+	0.873872i	$0.338399\pi$
$830$	−2709.17	+	3804.49i	−0.113297	+	0.159103i
$831$	3284.63	−	22919.0i	0.137115	−	0.956742i
$832$	−1905.90	−	5506.74i	−0.0794174	−	0.229462i
$833$	1702.14	−	877.516i	0.0707992	−	0.0364995i
$834$	11367.2	−	46949.5i	0.471960	−	1.94931i
$835$	−2334.34	+	1835.74i	−0.0967462	+	0.0760820i
$836$	3018.14	+	886.204i	0.124862	+	0.0366627i
$837$	−12652.7	−	36396.9i	−0.522510	−	1.50306i
$838$	2779.95	−	19335.0i	0.114596	−	0.797036i
$839$	−22966.1	+	2193.00i	−0.945028	+	0.0902392i	−0.556179	−	0.831062i	$-0.687733\pi$
$839$	−22966.1	+	2193.00i	−0.945028	+	0.0902392i	−0.388849	+	0.921302i	$0.627127\pi$
$840$	16956.0	−	3276.00i	0.696473	−	0.134563i
$841$	−1489.42	−	1171.29i	−0.0610694	−	0.0480255i
$842$	1653.68	+	34715.0i	0.0676835	+	1.42085i
$843$	−919.368	+	1061.98i	−0.0375620	+	0.0433887i
$844$	14196.3	−	11164.1i	0.578978	−	0.455314i
$845$	4173.80	+	4816.83i	0.169921	+	0.196099i
$846$	4710.30	+	32550.7i	0.191422	+	1.32283i
$847$	−12899.2	+	14886.4i	−0.523284	+	0.603901i
$848$	−18104.5	−	17262.6i	−0.733149	−	0.699056i
$849$	−1710.33	−	2959.28i	−0.0691384	−	0.119626i
$850$	2681.66	−	4644.78i	0.108212	−	0.187429i
$851$	35951.0	+	19666.2i	1.44816	+	0.792185i
$852$	13009.6	−	1248.23i	0.523123	−	0.0501922i
$853$	5514.06	−	7743.41i	0.221334	−	0.310820i	−0.688947	−	0.724812i	$-0.741927\pi$
$853$	5514.06	−	7743.41i	0.221334	−	0.310820i	0.910280	+	0.413992i	$0.135866\pi$
$854$	65.7661	−	19.3107i	0.00263521	−	0.000773768i
$855$	−54568.7	+	49.6223i	−2.18270	+	0.00198485i
$856$	4952.62	+	3182.86i	0.197754	+	0.127089i
$857$	11200.8	−	32362.7i	0.446456	−	1.28995i	−0.467448	−	0.884021i	$-0.654827\pi$
$857$	11200.8	−	32362.7i	0.446456	−	1.28995i	0.913904	−	0.405930i	$-0.133052\pi$
$858$	−5464.27	−	1601.76i	−0.217421	−	0.0637332i
$859$	1668.61	−	1591.02i	0.0662774	−	0.0631953i	−0.656217	−	0.754573i	$-0.727844\pi$
$859$	1668.61	−	1591.02i	0.0662774	−	0.0631953i	0.722494	+	0.691377i	$0.242996\pi$
$860$	305.442	+	6412.02i	0.0121110	+	0.254242i
$861$	−27387.0	+	14134.7i	−1.08403	+	0.559478i
$862$	−50550.4	+	4826.97i	−1.99739	+	0.190728i
$863$	−11872.0	+	25996.2i	−0.468284	+	1.02540i	0.517236	+	0.855843i	$0.326961\pi$
$863$	−11872.0	+	25996.2i	−0.468284	+	1.02540i	−0.985520	+	0.169557i	$0.945766\pi$
$864$	20059.3	+	7998.79i	0.789850	+	0.314959i
$865$	42388.7	−	27241.6i	1.66620	−	1.07080i
$866$	−5397.31	−	22248.0i	−0.211788	−	0.873001i
$867$	−17339.0	+	16547.8i	−0.679197	+	0.648203i
$868$	−15017.4	+	2894.36i	−0.587238	+	0.113181i
$869$	−4536.74	+	2338.85i	−0.177098	+	0.0913004i
$870$	−17560.1	−	38405.0i	−0.684302	−	1.49661i
$871$	−4541.21	−	4330.04i	−0.176663	−	0.168448i
$872$	−10457.4	−	22898.5i	−0.406115	−	0.889268i
$873$	2029.24	−	393.017i	0.0786704	−	0.0152367i
$874$	−38369.3	+	34826.8i	−1.48497	+	1.34786i
$875$	3844.28	+	6658.50i	0.148526	+	0.257255i
$876$	5067.96	+	8768.75i	0.195468	+	0.338206i
$877$	−8254.25	+	34024.5i	−0.317818	+	1.31006i	0.558971	+	0.829187i	$0.311196\pi$
$877$	−8254.25	+	34024.5i	−0.317818	+	1.31006i	−0.876789	+	0.480876i	$0.840319\pi$
$878$	13887.1	+	40124.3i	0.533791	+	1.54229i
$879$	−26552.1	−	13673.3i	−1.01886	−	0.524673i
$880$	2401.32	−	6938.17i	0.0919871	−	0.265779i
$881$	−4181.37	−	29082.1i	−0.159902	−	1.11214i	−0.898810	−	0.438338i	$-0.855567\pi$
$881$	−4181.37	−	29082.1i	−0.159902	−	1.11214i	0.738908	−	0.673807i	$-0.235342\pi$
$882$	5899.98	−	8301.32i	0.225241	−	0.316916i
$883$	−12483.6	+	8022.73i	−0.475772	+	0.305760i	−0.756461	−	0.654039i	$-0.773073\pi$
$883$	−12483.6	+	8022.73i	−0.475772	+	0.305760i	0.280689	+	0.959799i	$0.409437\pi$
$884$	3013.67	−	1206.49i	0.114661	−	0.0459035i
$885$	41504.0	+	47854.1i	1.57643	+	1.81763i
$886$	7403.45	+	10396.7i	0.280727	+	0.394226i
$887$	−5526.40	−	4346.01i	−0.209198	−	0.164515i	0.508063	−	0.861320i	$-0.330362\pi$
$887$	−5526.40	−	4346.01i	−0.209198	−	0.164515i	−0.717260	+	0.696805i	$0.754604\pi$
$888$	−26604.0	−	10636.6i	−1.00537	−	0.401960i
$889$	−3714.29	−	15310.5i	−0.140127	−	0.577613i
$890$	3838.44	+	26697.0i	0.144567	+	1.00549i
$891$	−3833.88	+	2473.75i	−0.144152	+	0.0930119i
$892$	−876.692	−	563.416i	−0.0329079	−	0.0211486i
$893$	48224.8	+	9294.56i	1.80714	+	0.348299i
$894$	39151.4	+	30760.2i	1.46467	+	1.15075i
$895$	−30369.4	−	2899.93i	−1.13423	−	0.108306i
$896$	−12344.7	+	21381.6i	−0.460275	+	0.797221i
$897$	21760.0	−	19769.0i	0.809971	−	0.735861i
$898$	20946.0	+	36279.5i	0.778369	+	1.34818i
$899$	−18497.7	−	40504.3i	−0.686244	−	1.50266i
$900$	417.238	−	8929.75i	0.0154533	−	0.330731i
$901$	−3554.07	+	4101.61i	−0.131413	+	0.151659i
$902$	−395.426	+	8301.02i	−0.0145967	+	0.306423i
$903$	6866.62	+	6541.35i	0.253053	+	0.241066i
$904$	−8690.74	−	3479.25i	−0.319745	−	0.128007i
$905$	−40033.9	+	38172.2i	−1.47047	+	1.40209i
$906$	−8815.24	+	6938.87i	−0.323253	+	0.254447i
$907$	−41830.7	+	16746.5i	−1.53139	+	0.613074i	−0.975854	−	0.218422i	$-0.929909\pi$
$907$	−41830.7	+	16746.5i	−1.53139	+	0.613074i	−0.555531	+	0.831496i	$0.687485\pi$
$908$	−3459.41	+	7575.06i	−0.126437	+	0.276858i
$909$	−5788.42	+	23955.2i	−0.211210	+	0.874087i
$910$	5579.64	−	38807.3i	0.203256	−	1.41368i
$911$	−19340.7	−	9970.85i	−0.703389	−	0.362622i	0.0691353	−	0.997607i	$-0.477976\pi$
$911$	−19340.7	−	9970.85i	−0.703389	−	0.362622i	−0.772524	+	0.634985i	$0.781006\pi$
$912$	37387.4	−	43187.1i	1.35748	−	1.56806i
$913$	541.366	+	216.730i	0.0196239	+	0.00785622i
$914$	−21298.0	+	4104.85i	−0.770759	+	0.148552i
$915$	4.82717	+	100.374i	0.000174406	+	0.00362653i
$916$	9523.57	+	1835.52i	0.343524	+	0.0662087i
$917$	15216.2	−	4467.87i	0.547963	−	0.160896i
$918$	2703.75	−	7846.59i	0.0972082	−	0.282109i
$919$	17362.2			0.623207			0.311603	−	0.950212i	$-0.399134\pi$
$919$	17362.2			0.623207			0.311603	+	0.950212i	$0.399134\pi$
$920$	15293.6	+	18551.4i	0.548061	+	0.664806i
$921$	−12508.4	−	17548.8i	−0.447521	−	0.627852i
$922$	−61219.6	−	5845.77i	−2.18673	−	0.208807i
$923$	−8328.88	+	34332.1i	−0.297019	+	1.22433i
$924$	753.027	+	1646.92i	0.0268104	+	0.0586359i
$925$	−1602.66	+	33644.0i	−0.0569677	+	1.19590i
$926$	39070.0	+	45089.1i	1.38652	+	1.60013i
$927$	16478.3	−	19051.9i	0.583838	−	0.675024i
$928$	23944.1	+	7030.62i	0.846987	+	0.248698i
$929$	9369.87	+	4830.51i	0.330910	+	0.170596i	0.615673	−	0.788002i	$-0.288884\pi$
$929$	9369.87	+	4830.51i	0.330910	+	0.170596i	−0.284762	+	0.958598i	$0.591915\pi$
$930$	3371.61	−	71462.3i	0.118881	−	2.51972i
$931$	−8821.36	−	12387.9i	−0.310535	−	0.436086i
$932$	−134.509	−	188.892i	−0.00472746	−	0.00663879i
$933$	327.732	−	6946.39i	0.0115000	−	0.243746i
$934$	47656.1	+	24568.4i	1.66954	+	0.860710i
$935$	−1528.36	−	448.766i	−0.0534573	−	0.0156965i
$936$	−13446.8	+	15547.0i	−0.469575	+	0.542916i
$937$	−5051.62	−	5829.88i	−0.176125	−	0.203259i	0.660822	−	0.750542i	$-0.270208\pi$
$937$	−5051.62	−	5829.88i	−0.176125	−	0.203259i	−0.836948	+	0.547283i	$0.815662\pi$
$938$	−302.957	+	6359.84i	−0.0105457	+	0.221382i
$939$	−1561.32	−	3414.70i	−0.0542617	−	0.118674i
$940$	−4512.00	+	18598.7i	−0.156559	+	0.645344i
$941$	−33478.4	−	3196.80i	−1.15979	−	0.110747i	−0.502634	−	0.864499i	$-0.667636\pi$
$941$	−33478.4	−	3196.80i	−1.15979	−	0.110747i	−0.657158	+	0.753753i	$0.728242\pi$
$942$	15309.3	+	21478.2i	0.529515	+	0.742885i
$943$	−35514.9	−	24076.6i	−1.22643	−	0.831433i
$944$	−66309.1			−2.28621
$945$	−20605.1	−	23714.1i	−0.709296	−	0.816318i
$946$	2453.67	−	720.463i	0.0843296	−	0.0247614i
$947$	−23960.6	−	4618.02i	−0.822189	−	0.158464i	−0.239228	−	0.970964i	$-0.576894\pi$
$947$	−23960.6	−	4618.02i	−0.822189	−	0.158464i	−0.582962	+	0.812500i	$0.698106\pi$
$948$	−743.349	−	15456.9i	−0.0254671	−	0.529555i
$949$	−26882.3	+	5181.14i	−0.919533	+	0.177225i
$950$	−39540.7	−	15829.7i	−1.35039	−	0.540615i
$951$	−1918.63	+	2216.26i	−0.0654216	+	0.0755699i
$952$	3486.05	+	1797.18i	0.118680	+	0.0611838i
$953$	205.639	−	1430.25i	0.00698982	−	0.0486153i	−0.986028	−	0.166580i	$-0.946728\pi$
$953$	205.639	−	1430.25i	0.00698982	−	0.0486153i	0.993018	+	0.117964i	$0.0376368\pi$
$954$	−6779.12	+	28055.3i	−0.230065	+	0.952120i
$955$	−5925.28	+	12974.5i	−0.200772	+	0.439630i
$956$	−13529.8	+	5416.52i	−0.457726	+	0.183246i
$957$	−4143.00	+	3261.14i	−0.139942	+	0.110154i
$958$	−46781.1	+	44605.7i	−1.57769	+	1.50433i
$959$	7776.87	+	3113.39i	0.261865	+	0.104835i
$960$	−6276.83	−	5979.49i	−0.211025	−	0.201028i
$961$	2171.92	−	45594.1i	0.0729051	−	1.53047i
$962$	−42596.2	+	49158.7i	−1.42761	+	1.64755i
$963$	499.852	−	10697.9i	0.0167264	−	0.357979i
$964$	3472.89	+	7604.57i	0.116031	+	0.254073i
$965$	−30398.7	−	52652.0i	−1.01406	−	1.75640i
$966$	−29619.8	−	3550.65i	−0.986543	−	0.118261i
$967$	23856.5	−	41320.7i	0.793354	−	1.37413i	−0.130525	−	0.991445i	$-0.541666\pi$
$967$	23856.5	−	41320.7i	0.793354	−	1.37413i	0.923879	−	0.382685i	$-0.125000\pi$
$968$	19086.9	+	1822.58i	0.633756	+	0.0605164i
$969$	−9744.99	−	7656.38i	−0.323069	−	0.253827i
$970$	3768.18	+	726.257i	0.124731	+	0.0240399i
$971$	32996.7	+	21205.7i	1.09054	+	0.700848i	0.956969	−	0.290191i	$-0.0937188\pi$
$971$	32996.7	+	21205.7i	1.09054	+	0.700848i	0.133572	+	0.991039i	$0.457355\pi$
$972$	−1999.79	−	13687.9i	−0.0659911	−	0.451686i
$973$	−5909.90	−	41104.3i	−0.194720	−	1.35431i
$974$	9695.81	+	39966.7i	0.318967	+	1.31480i
$975$	22437.7	+	8970.85i	0.737005	+	0.294664i
$976$	−82.6870	−	65.0258i	−0.00271183	−	0.00213261i
$977$	−19401.2	−	27245.1i	−0.635311	−	0.892169i	0.363918	−	0.931431i	$-0.381439\pi$
$977$	−19401.2	−	27245.1i	−0.635311	−	0.892169i	−0.999229	+	0.0392618i	$0.987499\pi$
$978$	23877.7	+	27531.0i	0.780700	+	0.900149i
$979$	3126.30	−	1251.58i	0.102060	−	0.0408588i
$980$	4985.43	−	3203.94i	0.162504	−	0.104435i
$981$	−26528.9	+	37326.4i	−0.863407	+	1.21482i
$982$	3510.39	+	24415.3i	0.114075	+	0.793406i
$983$	−7062.77	+	20406.5i	−0.229163	+	0.662123i	0.770531	+	0.637402i	$0.219991\pi$
$983$	−7062.77	+	20406.5i	−0.229163	+	0.662123i	−0.999694	+	0.0247211i	$0.992130\pi$
$984$	26671.1	+	13734.6i	0.864068	+	0.444961i
$985$	−2973.70	−	8591.94i	−0.0961929	−	0.277931i
$986$	2261.05	−	9320.19i	0.0730290	−	0.301030i
$987$	14148.2	+	24479.7i	0.456274	+	0.789460i
$988$	−12889.5	−	22325.2i	−0.415050	−	0.718887i
$989$	−3426.91	+	12750.6i	−0.110182	+	0.409956i
$990$	−8316.61	+	1610.74i	−0.266989	+	0.0517098i
$991$	−9484.69	−	20768.6i	−0.304027	−	0.665727i	0.694528	−	0.719466i	$-0.255613\pi$
$991$	−9484.69	−	20768.6i	−0.304027	−	0.665727i	−0.998555	+	0.0537391i	$0.982886\pi$
$992$	30597.3	+	29174.5i	0.979300	+	0.933761i
$993$	−15975.0	−	34938.3i	−0.510525	−	1.11655i
$994$	31862.9	−	16426.5i	1.01673	−	0.524161i
$995$	44606.6	−	8597.22i	1.42123	−	0.273920i
$996$	−1278.98	+	1220.62i	−0.0406888	+	0.0388321i
$997$	6596.73	+	27192.1i	0.209549	+	0.863773i	0.975344	+	0.220689i	$0.0708305\pi$
$997$	6596.73	+	27192.1i	0.209549	+	0.863773i	−0.765795	+	0.643085i	$0.777654\pi$
$998$	−5035.73	+	3236.27i	−0.159723	+	0.102648i
$999$	7487.90	+	51580.0i	0.237144	+	1.63355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.m.a.4.17	✓	1400
9.7	even	3	inner	207.4.m.a.142.54	yes	1400
23.6	even	11	inner	207.4.m.a.121.54	yes	1400
207.52	even	33	inner	207.4.m.a.52.17	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.m.a.4.17	✓	1400	1.1	even	1	trivial
207.4.m.a.52.17	yes	1400	207.52	even	33	inner
207.4.m.a.121.54	yes	1400	23.6	even	11	inner
207.4.m.a.142.54	yes	1400	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98001 + 2.78054i) q^{2} +(-4.08591 - 3.21019i) q^{3} +(-1.19440 - 3.45100i) q^{4} +(13.0530 - 6.72929i) q^{5} +(17.0162 - 5.00482i) q^{6} +(11.9856 - 9.42560i) q^{7} +(-14.2411 - 4.18156i) q^{8} +(6.38935 + 26.2331i) q^{9} +(-7.13406 + 49.6185i) q^{10} +(6.23048 - 0.594938i) q^{11} +(-6.19815 + 17.9348i) q^{12} +(-40.3193 - 31.7074i) q^{13} +(2.47656 + 51.9893i) q^{14} +(-74.9357 - 14.4073i) q^{15} +(62.7890 - 49.3778i) q^{16} +(-11.3488 - 13.0972i) q^{17} +(-85.5932 - 34.1761i) q^{18} +(-90.1240 + 104.009i) q^{19} +(-38.8134 - 37.0085i) q^{20} +(-79.2302 + 0.0360241i) q^{21} +(-10.6822 + 18.5021i) q^{22} +(-52.7895 - 96.8518i) q^{23} +(44.7643 + 62.8022i) q^{24} +(52.5904 - 73.8528i) q^{25} +(167.996 - 49.3282i) q^{26} +(58.1070 - 127.697i) q^{27} +(-46.8435 - 30.1045i) q^{28} +(53.0252 - 153.206i) q^{29} +(188.434 - 179.835i) q^{30} +(198.779 - 189.535i) q^{31} +(7.32410 + 153.752i) q^{32} +(-27.3670 - 17.5702i) q^{33} +(58.8881 - 5.62313i) q^{34} +(93.0208 - 203.687i) q^{35} +(82.8991 - 53.3826i) q^{36} +(-312.529 + 200.850i) q^{37} +(-110.753 - 456.532i) q^{38} +(62.9541 + 258.986i) q^{39} +(-214.028 + 41.2505i) q^{40} +(345.745 - 178.244i) q^{41} +(156.777 - 220.374i) q^{42} +(-86.6292 - 82.6007i) q^{43} +(-9.49484 - 20.7908i) q^{44} +(259.930 + 299.425i) q^{45} +(373.824 + 44.9844i) q^{46} +(-178.430 - 309.050i) q^{47} +(-415.062 + 0.188719i) q^{48} +(-26.0520 + 107.388i) q^{49} +(101.221 + 292.459i) q^{50} +(4.32564 + 89.9459i) q^{51} +(-61.2649 + 177.013i) q^{52} +(-44.5682 - 309.979i) q^{53} +(240.015 + 414.411i) q^{54} +(77.3229 - 49.6924i) q^{55} +(-210.102 + 84.1122i) q^{56} +(702.126 - 135.655i) q^{57} +(321.005 + 450.789i) q^{58} +(-652.520 - 513.147i) q^{59} +(39.7837 + 275.812i) q^{60} +(-0.310472 - 1.27978i) q^{61} +(133.426 + 927.996i) q^{62} +(323.843 + 254.197i) q^{63} +(95.5716 + 61.4201i) q^{64} +(-739.656 - 142.557i) q^{65} +(103.042 - 41.3060i) q^{66} +(121.776 + 11.6282i) q^{67} +(-31.6435 + 54.8081i) q^{68} +(-95.2192 + 565.192i) q^{69} +(382.178 + 661.951i) q^{70} +(-286.115 - 626.503i) q^{71} +(18.7041 - 400.306i) q^{72} +(349.522 - 403.370i) q^{73} +(60.3397 - 1266.69i) q^{74} +(-451.961 + 132.931i) q^{75} +(466.579 + 186.790i) q^{76} +(69.0685 - 65.8567i) q^{77} +(-844.772 - 337.750i) q^{78} +(-757.094 + 303.095i) q^{79} +(487.307 - 1067.05i) q^{80} +(-647.352 + 335.225i) q^{81} +(-188.965 + 1314.28i) q^{82} +(82.8133 + 42.6932i) q^{83} +(94.7572 + 273.381i) q^{84} +(-236.271 - 94.5886i) q^{85} +(401.202 - 77.3253i) q^{86} +(-708.477 + 455.766i) q^{87} +(-91.2166 - 17.5806i) q^{88} +(516.250 - 151.585i) q^{89} +(-1347.23 + 129.881i) q^{90} -782.113 q^{91} +(-271.184 + 297.857i) q^{92} +(-1420.64 + 136.306i) q^{93} +(1212.62 + 115.791i) q^{94} +(-476.484 + 1964.09i) q^{95} +(463.647 - 651.728i) q^{96} +(3.64256 - 76.4668i) q^{97} +(-247.013 - 285.068i) q^{98} +(55.4158 + 159.644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) \) 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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